{"id":2698,"date":"2022-03-24T11:42:28","date_gmt":"2022-03-24T11:42:28","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2698"},"modified":"2022-03-24T05:56:02","modified_gmt":"2022-03-24T05:56:02","slug":"gausss-law","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/gausss-law\/","title":{"rendered":"\u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Gauss’s law)"},"content":{"rendered":"

\u099c\u09be\u09b0\u09cd\u09ae\u09be\u09a8 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u0995\u09be\u09b0\u09cd\u09b2 \u09ab\u09cd\u09b0\u09c7\u09a1\u09b0\u09bf\u0995 \u0997\u09be\u0989\u09b8 (Carl Friedrich Gauss)<\/strong> \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 \u0993 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u098f\u0995\u099f\u09bf \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a6\u09be\u09a8 \u0995\u09b0\u09c7\u09a8\u0964 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09ac\u09be\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u098f \u09b8\u09c2\u09a4\u09cd\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09c3\u09a4 \u09b9\u09af\u09bc\u0964 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09ac\u09bf\u09ac\u09c3\u09a4 \u0995\u09b0\u09be\u09b0 \u0986\u0997\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8, \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0993 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 \u0995\u09c0 \u099c\u09be\u09a8\u09be \u09a6\u09b0\u0995\u09be\u09b0\u0964<\/span><\/p>\n

\u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 (<\/b>Electric flux)<\/b><\/h2>\n

\u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0995\u09cb\u09a8\u09cb \u09a4\u09b2\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af \u09a6\u09bf\u09af\u09bc\u09c7 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09ac\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964<\/b> \u098f\u0995\u09c7 \\varphi<\/span> <\/span>(phi)\u00a0<\/span>\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 <\/span>\u098f\u0995\u099f\u09bf \u09b8\u09cd\u0995\u09c7\u09b2\u09be\u09b0 \u09b0\u09be\u09b6\u09bf\u0964 \u098f\u09b0 \u098f\u0995\u0995 \u0993\u09af\u09bc\u09c7\u09ac\u09be\u09b0 (W b)<\/span><\/span>\u00a0\u09ac\u09be <\/span>Tesla<\/span>\u00a0 m^{2}<\/span><\/span>\u00a0<\/span>\u09ac\u09be<\/span> N m^{-1} A<\/span>\u00a0<\/span> \u09ac\u09be <\/span>N C^{-1} m^{2}<\/span><\/span>\u00a0<\/span>\u0964<\/span><\/p>\n

\u0985\u09a8\u09cd\u09af\u09ad\u09be\u09ac\u09c7 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u0995\u09cb\u09a8\u09cb \u09a4\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u098f\u09ac\u0982 \u0993\u0987 \u09a4\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0989\u09aa\u09be\u0982\u09b6\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u0995\u09c7 \u0993\u0987 \u09a4\u09b2\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u0982\u09b6\u09cd\u09b2\u09bf\u09b7\u09cd\u099f \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964 \u0995\u09cb\u09a8\u09cb \u09a4\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 <\/span>S<\/span><\/span> \u098f\u09ac\u0982 \u0993\u0987 \u09a4\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>E<\/span><\/span> \u09b9\u09b2\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 <\/span>\\varphi<\/span> = E S<\/span><\/span><\/p>\n

\"Electric <\/b>\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be (Explanation):<\/b><\/h3>\n

\\vec{E}<\/span><\/span>\u00a0<\/span>\u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2 S<\/span> \u098f\u09b0 \u0993\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 d \\vec{S}<\/span><\/span>\u00a0\u09a8\u09c7\u09af\u09bc\u09be \u09b9\u09b2\u09cb [\u099a\u09bf\u09a4\u09cd\u09b0 \u09e8.\u09e8\u09ef]\u0964 <\/span>\\vec{E}<\/span><\/span> \u0993 d \\vec{S}<\/span><\/span>\u00a0\u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09a3 \u09b9\u09b2\u09cb \\theta<\/span> <\/span>\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982, d \\vec{S}<\/span><\/span>\u00a0\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af \u09a6\u09bf\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8,\u00a0<\/span><\/p>\n\\begin{aligned}\n\nd \\varphi &=\\vec{E} \\cdot d \\vec{S} \\\\\n\n&=E d S \\cos \\theta \\\\\n\n&=(E \\cos \\theta) d S=E_{n} d S \\quad \\ldots\n\n\\end{aligned}<\/span>\n

\u098f\u0996\u09be\u09a8\u09c7\u00a0 E_{n}=E \\cos \\theta=<\/span><\/span>\u00a0\u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af\u09c7\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u0989\u09aa\u09be\u0982\u09b6\u0964<\/span><\/p>\n

\u098f\u0996\u09a8, \u09b8\u09ae\u0997\u09cd\u09f0 \u09a4\u09b2\u099f\u09bf \u098f\u09b0\u09c2\u09aa \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09f0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09f0 d \\vec{S}<\/span><\/span>\u098f\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u0997\u09cd\u09b0 <\/span>S<\/span><\/span> \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af \u09a6\u09bf\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7 \\varphi=\\oint \\vec{E} \\cdot d \\vec{S}<\/span><\/span><\/p>\n

\\oint<\/span> <\/span>\u09aa\u09cd\u09b0\u09a4\u09c0\u0995\u099f\u09bf \u09b8\u09ae\u0997\u09cd\u09b0 \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 (<\/b>Area vector)<\/b><\/h2>\n

\u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09aa\u09c3\u09b7\u09cd\u09a0\u09a4\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u0997\u09a3\u09cd\u09af \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u099f\u09bf\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09a4\u09b2\u099f\u09bf\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u098f\u09ac\u0982 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u099f\u09bf\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u09a7\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u09b2\u099f\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0\u0964<\/span><\/p>\n

\"\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0<\/b>\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be (Explanation):<\/b><\/h3>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995 <\/span>s<\/span><\/span> \u098f\u0995\u099f\u09bf \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u0964 \u098f\u09b0 \u0993\u09aa\u09b0\u09c7 <\/span>d \\vec{S}<\/span><\/span> \u098f\u0995\u099f\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u0964 d S<\/span><\/span> \u098f\u09b0 \u0993\u09aa\u09b0 \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09be \u09b9\u09b2\u09cb\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 d \\vec{S}<\/span><\/span>\u00a0\u09b9\u09b2\u09cb \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995 \u09a4\u09b2 \u09a5\u09c7\u0995\u09c7 \u09a4\u09b2\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09a7\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 (Gaussian surface) :<\/b><\/h2>\n

\u098f\u0995\u099f\u09bf \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u099a\u09be\u09b0\u09a6\u09bf\u0995\u09c7 \u0995\u09b2\u09cd\u09aa\u09bf\u09a4 \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u0995\u09c7 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Gauss’s law) :<\/b><\/h3>\n

\u0995\u09cb\u09a8\u09cb \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0995\u09cb\u09a8\u09cb \u09ac\u09a6\u09cd\u09a7 \u0995\u09b2\u09cd\u09aa\u09bf\u09a4 \u09a4\u09b2\u09c7\u09b0<\/b> \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 \u0993\u0987 \u09a4\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ac\u09c7\u09b7\u09cd\u099f\u09bf\u09a4 \u09ae\u09cb\u099f \u0986\u09a7\u09be\u09a8\u09c7\u09b0<\/b> \\frac{1}{\\epsilon_{o}}<\/span> \u0997\u09c1\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09ac\u09c7\u0964<\/b><\/p>\n

\u0985\u09a8\u09cd\u09af\u09ad\u09be\u09ac\u09c7 \u0995\u09cb\u09a8\u09cb \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09a6\u09cd\u09a7 \u0995\u09b2\u09cd\u09aa\u09bf\u09a4 \u09a4\u09b2\u09c7\u09b0 (\u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7\u09b0) \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8\u09c7\u09b0<\/span> \\epsilon_{o}<\/span><\/span>\u00a0\u0997\u09c1\u09a3 \u09b9\u09ac\u09c7 \u0993\u0987 \u09a4\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0986\u09ac\u09a6\u09cd\u09a7 \u09ae\u09cb\u099f \u09a4\u09a1\u09bc\u09bf\u09a4\u09be\u09a7\u09be\u09a8\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964 \u098f\u0996\u09be\u09a8\u09c7 <\/span>\\epsilon_{o}<\/span><\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09b6\u09c2\u09a8\u09cd\u09af \u09b8\u09cd\u09a5\u09be\u09a8\u09c7\u09b0 \u09ad\u09c7\u09a6\u09a8\u09af\u09cb\u0997\u09cd\u09af\u09a4\u09be<\/strong>\u0964<\/span><\/p>\n

\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be (Explanation):\u00a0<\/b><\/h4>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995<\/span>, <\/span>\u09b6\u09c2\u09a8\u09cd\u09af \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 <\/span>S<\/span><\/span> \u098f\u09ac\u0982 \u0993\u0987 \u09a4\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0986\u09ac\u09a6\u09cd\u09a7 \u09ae\u09cb\u099f \u0986\u09a7\u09be\u09a8 <\/span>q<\/span><\/span>\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7<\/span>,<\/span><\/p>\n\\epsilon_{o} \\varphi=q<\/span>\n

\\epsilon_{o} \\oint \\vec{E} \\cdot d \\vec{S}=q<\/span>\u00a0<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>\\epsilon_{o}<\/span><\/span> \u09b9\u09b2\u09cb \u09b6\u09c2\u09a8\u09cd\u09af \u09b8\u09cd\u09a5\u09be\u09a8\u09c7\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ad\u09c7\u09a6\u09a8\u09af\u09cb\u0997\u09cd\u09af\u09a4\u09be (permittivity)<\/strong>\u0964 \u0985\u09a8\u09cd\u09af \u0995\u09cb\u09a8\u09cb \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09ac\u09c7,<\/span><\/p>\n

\\epsilon \\oint \\vec{E} \\cdot d \\vec{S}=q<\/span> \u098f\u0996\u09be\u09a8\u09c7 \\epsilon<\/span>\u00a0<\/span> \u09b9\u09b2\u09cb \u0993\u0987 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ad\u09c7\u09a6\u09a8\u09af\u09cb\u0997\u09cd\u09af\u09a4\u09be\u0964\u00a0<\/span><\/p>\n

\u09ac\u09bf. \u09a6\u09cd\u09b0. <\/b>\u09af\u09a6\u09bf \u0997\u09be\u0989\u09b8\u09c0\u09df \u09a4\u09b2\u09c7 \u0995\u09cb\u09a8\u09cb \u0986\u09a7\u09be\u09a8 \u09a8\u09be \u09a5\u09be\u0995\u09c7 \u0985\u09a5\u09ac\u09be \u09b8\u09ae\u09b8\u0982\u0996\u09cd\u09af\u0995 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u0993 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0986\u09a7\u09be\u09a8 \u09a5\u09be\u0995\u09c7, \u09a4\u09ac\u09c7<\/span><\/p>\n

\\varphi=\\oint \\vec{E} \\cdot d \\vec{S}=0<\/span> \u09b9\u09ac\u09c7.<\/p>\n

\u0997\u09be\u0989\u09b8 (Gauss)<\/b><\/h3>\n

\u0997\u09be\u0989\u09b8 \u09b9\u09b2\u09cb \u099a\u09cc\u09ae\u09cd\u09ac\u0995 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u098f\u0995\u0995<\/strong>\u0964 \u0985\u09ac\u09b6\u09cd\u09af \u098f\u099f\u09bf \u098f\u09b8<\/span>.<\/span> \u0986\u0987<\/span>.<\/span> \u098f\u0995\u0995 \u09a8\u09af\u09bc\u0964 \u099f\u09c7\u09b8\u09b2\u09be (T)<\/span><\/span>\u00a0<\/span>\u09ac\u09be<\/span>\u00a0\u0993\u09af\u09bc\u09c7\u09ac\u09be\u09b0 \/ \\text {\u09ae\u09bf\u099f\u09be\u09b0}^2<\/span><\/span> \u09b9\u09b2\u09cb \u098f\u09b8. \u0986\u0987. \u098f\u0995\u0995\u0964 1 T=10^{4} gauss<\/span><\/span>\u00a0\u0964<\/span><\/p>\n

\u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 <\/b>(Derivation of Gauss’s law from Coulomb’s law)<\/b><\/h2>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, <\/span>O<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 +q<\/span><\/span>\u00a0<\/span>\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0986\u09a7\u09be\u09a8\u0995\u09c7 \u0998\u09bf\u09b0\u09c7 S<\/span><\/span>\u00a0\u098f\u0995\u099f\u09bf \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2 (\u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2) [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u0993\u0987 \u09a4\u09b2\u09c7\u09b0 \u0993\u09aa\u09b0\u09c7 <\/span>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0995\u09c7 \u0998\u09bf\u09b0\u09c7 <\/span>d S<\/span><\/span> \u098f\u0995\u099f\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09a4\u09b2 \u0995\u09b2\u09cd\u09aa\u09a8\u09be \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0986\u09a7\u09be\u09a8 +q<\/span><\/span>\u00a0\u098f\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/span>\\vec{E}<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <\/span>O P<\/span><\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0\u0964<\/span><\/p>\n

\"Derivation<\/b>\u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 <\/span>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf \u098f\u0995\u0995 \u0986\u09a7\u09be\u09a8 \u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09b2\u09c7 \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0 \u0993\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af, E=\\frac{1}{4 \\pi \\epsilon_{o} r^{2}}<\/span><\/span>\u00a0<\/span>\u098f\u09b0 \u09a6\u09bf\u0995 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0\u0964<\/span><\/p>\n

\u098f\u0996\u09a8, <\/span>d S<\/span><\/span> \u09a4\u09b2\u09c7 \u09ae\u09cb\u099f \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8,<\/span><\/p>\n

d \\varphi=\\vec{E} \\cdot d \\vec{S}=E d S \\cos \\theta<\/span> \u00a0<\/span><\/p>\n

\u09ac\u09be, d \\varphi=\\frac{q}{4 \\pi \\epsilon_{o} r^{2}} d S \\cos \\theta \\quad<\/span><\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 \\theta<\/span> <\/span>\u09b9\u09b2\u09cb d \\vec{S}<\/span><\/span>\u00a0<\/span>\u0993 <\/span>\\vec{E}<\/span><\/span> \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a3\u0964<\/span><\/p>\n

\u09ac\u09be, d \\varphi=\\frac{q}{4 \\pi \\epsilon_{o}} \\cdot \\frac{d S \\cos \\theta}{r^{2}}=\\frac{q}{4 \\pi \\epsilon_{o}} d \\omega<\/span><\/span><\/p>\n

d \\omega<\/span><\/span> \u09b9\u099a\u09cd\u099b\u09c7 <\/span>d S<\/span><\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09f0 \u09a4\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af<\/span> O<\/span> <\/span>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0998\u09a8\u0995\u09cb\u09a3<\/strong>\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u09b8\u09ae\u0997\u09cd\u09b0 \u0986\u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2 <\/span>S<\/span><\/span>-\u098f\u09b0 \u099c\u09a8\u09cd\u09af \u09ae\u09cb\u099f \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8,\u00a0<\/span><\/p>\n\\begin{aligned}\n\n\\varphi &=\\oint d \\varphi=\\oint \\vec{E} \\cdot d \\vec{S} \\\\\n\n&=\\oint \\frac{q}{4 \\pi \\epsilon_{o}} d \\omega=\\frac{q}{4 \\pi \\epsilon_{o}} \\oint d \\omega \\\\\n\n&=\\frac{q}{4 \\pi \\epsilon_{o}} \\omega=\\frac{q}{4 \\pi \\epsilon_{o}} \\times 4 \\pi =\\frac{q}{\\epsilon_{o}} \\end{aligned}<\/span>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>\\oint d \\omega=\\omega=4 \\pi<\/span><\/span> \u09b8\u09cd\u099f\u09c7\u09b0\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09a8 (Steradian) \\omega<\/span> <\/span>\u09b9\u099a\u09cd\u099b\u09c7 \\circ<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09ae\u0997\u09cd\u09b0 \u09a4\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u09ae\u09cb\u099f \u0998\u09a8\u0995\u09cb\u09a3\u0964<\/span><\/p>\n\\varphi=\\frac{q}{\\epsilon_{o}}<\/span>\n

\u09ac\u09be,\u00a0 \\oint \\vec{E} \\cdot d \\vec{S}=\\frac{q}{\\epsilon_{o}}<\/span><\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u0987 \u09b9\u09b2\u09cb \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0964 \u0987\u09b9\u09be \u099a\u09be\u09b0\u09cd\u099c \u098f\u09ac\u0982 \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u0997\u09be\u0989\u09b8\u09c7 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 <\/b>(Deduction of Coulomb’s law from Gauss’s law)<\/b><\/h2>\n

\"Deduction<\/b>\u09a7\u09b0\u09be \u09af\u09be\u0995, <\/span>O<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09cd\u09a5\u09be\u09aa\u09bf\u09a4 <\/span>+q<\/span><\/span> \u099a\u09be\u09b0\u09cd\u099c \u09b9\u09a4\u09c7 <\/span>r<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 <\/span>P<\/span><\/span> \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964 \u098f\u0996\u09a8 <\/span>q<\/span><\/span>-\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 <\/span>r<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09be\u09ae\u09cd\u09af \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be\u09af\u09bc \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c +q<\/span><\/span>\u00a0\u098f\u09b0 \u099c\u09a8\u09cd\u09af <\/span>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/span>\\vec{E}<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0\u0964 \u098f\u0987 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09aa\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u098f\u09ac\u0982 \u09b8\u09b0\u09cd\u09ac\u09a4\u09cd\u09b0 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 d \\vec{S}<\/span><\/span>\u00a0<\/span>\u0993 <\/span>\\vec{E}<\/span><\/span> \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \\vec{E} \\cdot d \\vec{S}=E d S \\cos 0^{\\circ}=E d S<\/span><\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ae\u09cb\u099f \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8,<\/span><\/p>\n\\begin{aligned} \\varphi &=\\oint \\vec{E} \\cdot d \\vec{S}=\\frac{q}{\\epsilon_{o}} \\\\ &=E \\oint d S \\quad \\quad[\\because \\text { \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a } E \\text {\u09a7\u09cd\u09b0\u09c1\u09ac\u0995] }\\\\ &=E .4 \\pi r^{2}=\\frac{q}{\\epsilon_{0}} \\end{aligned}<\/span>\n

\u00a0 =E .4 \\pi r^{2}=\\frac{q}{\\epsilon_{0}}<\/span><\/span><\/p>\n

\u09ac\u09be,\u00a0 E=\\frac{q}{4 \\pi \\epsilon_{o} r^{2}}<\/span><\/span><\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, <\/span>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf \u099a\u09be\u09b0\u09cd\u099c q_{0}<\/span><\/span> \u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 q_{0}<\/span><\/span>\u00a0<\/span>\u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u0993\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u09ac\u09b2,<\/span><\/p>\n\\begin{array}{l}\n\n\\mathrm{F}=q_{0} E \\\\\n\n\\mathrm{~F}=\\frac{q q_{0}}{4 \\pi \\epsilon_{0} r^{2}}\n\n\\end{array}<\/span>\n

\u098f\u099f\u09bf\u0987 \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09bf\u09a4 \u09b9\u09b2\u09cb\u0964<\/span><\/p>\n

\u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 (<\/b>Applications of Gauss’s law to determine the electric field intensity)<\/b><\/h2>\n

\u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u09a8\u09bf\u09ae\u09cd\u09a8\u09c7 \u0995\u09af\u09bc\u09c7\u0995\u099f\u09bf \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a4\u09be \u09ac\u09b0\u09cd\u09a3\u09a8\u09be \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964<\/span><\/p>\n

(\u0995) \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/b>(The electric field intensity due to the charged sphere)<\/b><\/h3>\n

R<\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09c7\u099f \u0997\u09cb\u09b2\u0995 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995\u0964 \u0997\u09cb\u09b2\u0995\u09c7 +q<\/span><\/span>\u00a0\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u099a\u09be\u09b0\u09cd\u099c \u09aa\u09cd\u09b0\u09a6\u09be\u09a8 \u0995\u09b0\u09b2\u09c7 \u098f\u0987 \u099a\u09be\u09b0\u09cd\u099c \u09b8\u09c1\u09b7\u09ae\u09ad\u09be\u09ac\u09c7 \u0997\u09cb\u09b2\u0995 \u09aa\u09c3\u09b7\u09cd\u09a0\u09c7 \u099b\u09a1\u09bc\u09bf\u09af\u09bc\u09c7 \u09aa\u09a1\u09bc\u09ac\u09c7\u0964 \u0995\u09cb\u09a8\u09cb \u099a\u09be\u09b0\u09cd\u099c \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ad\u09c7\u09a4\u09b0\u09c7 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09ac\u09c7 \u09a8\u09be\u0964 \u098f\u0996\u09a8 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0989\u0995\u09cd\u09a4 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 <\/span>r<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u0995\u099f\u09be \u0997\u09cb\u09b2\u0995\u09c0\u09af\u09bc \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995\u0964 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09be\u09ae\u09cd\u09af\u09c7\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a4\u09cd\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>E<\/span>-\u098f\u09b0 \u09ae\u09be\u09a8 \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u09a6\u09bf\u0995 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964 \u09a4\u09ac\u09c7 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 \u0995\u09cb\u09a8\u09cb \u099a\u09be\u09b0\u09cd\u099c \u09a7\u09be\u09b0\u09a3 \u0995\u09b0\u09ac\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

\\begin{array}{c}\n\n\\oint_{s} \\vec{E} \\cdot d \\vec{a}=\\oint_{s} E d a=E \\oint d a \\\\\n\n=E\\left(4 \\pi r^{2}\\right)=0 \\\\\n\n\\therefore E=0 . .\n\n\\end{array}<\/span><\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>r<R<\/span> <\/span>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af\u0964<\/span><\/p>\n

\"\u09a4\u09a1\u09bc\u09bf\u09ce<\/b>\u0986\u09ac\u09be\u09b0, <\/span>r>R<\/span> <\/span>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09f0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0989\u0995\u09cd\u09a4 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 r<\/span><\/span>\u00a0<\/span>\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u0997\u09cb\u09b2\u09c0\u09af\u09bc \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 \u0995\u09b2\u09cd\u09aa\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u098f\u0987 \u09a4\u09b2 \u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u0986\u09ac\u09a6\u09cd\u09a7 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09b9\u09ac\u09c7 <\/span>q<\/span><\/span>\u0964<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a4\u09cd\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \\vec{E}<\/span><\/span>\u00a0\u09b8\u09c1\u09b7\u09ae \u09ae\u09be\u09a8\u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09ac\u09c7\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\oint_{s} \\vec{E} \\cdot d \\vec{a}=E\\left(4 \\pi r^{2}\\right)=\\frac{q}{\\epsilon_{o}}<\/span>\n

\u09ac\u09be,\u00a0 E=\\frac{q}{4 \\pi \\epsilon_{o} r^{2}}<\/span><\/span><\/p>\n

\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0986\u0995\u09be\u09b0\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987, <\/span>\\vec{E}<\/span> <\/span>=\\frac{q}{4 \\pi \\epsilon_{o} r^{3}} \\vec{r}<\/span><\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc, \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09ac\u09b9\u09bf\u09b8\u09cd\u09a5 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u09b0 \u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, \u09ac\u09b9\u09bf\u09b8\u09cd\u09a5 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09f0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c \u098f\u09ae\u09a8 \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7 \u09af\u09c7, \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u099a\u09be\u09b0\u09cd\u099c \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09ad\u09c2\u09a4 \u09a5\u09c7\u0995\u09c7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a8\u09cd\u09af\u09be\u09af\u09bc \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7\u0964 \u09af\u09a6\u09bf \u0997\u09cb\u09b2\u0995\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a4\u09b2 \u0998\u09a8\u09a4\u09cd\u09ac <\/span> \u09b9\u09af\u09bc \\sigma<\/span> \u09a4\u09ac\u09c7 \\sigma=\\frac{q}{4 \\pi r^{2}}<\/span><\/span> \u09b9\u09ac\u09c7\u0964 \u0985\u09a4\u098f\u09ac, \\vec{E}=\\frac{\\sigma}{\\epsilon_{o}} \\hat{n}<\/span><\/span>\u00a0<\/span><\/p>\n

\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0986\u0995\u09be\u09b0\u09c7, E=\\frac{\\sigma}{\\epsilon_{o}}<\/span><\/span><\/p>\n

\u09af\u09c7\u0996\u09be\u09a8\u09c7 \\hat{n}<\/span><\/span>\u00a0\u09b9\u09b2\u09cb \u09aa\u09c3\u09b7\u09cd\u09a0\u09c7\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u098f\u0995\u0995 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0964<\/span><\/p>\n

(\u0996) \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u098f\u0995\u099f\u09be \u09b2\u09ae\u09cd\u09ac\u09be \u099a\u09cb\u0999\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/b>(Electric field intensity due to charged tube)<\/b><\/h3>\n

\u09b8\u09c1\u09b7\u09ae\u09ad\u09be\u09ac\u09c7 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 <\/span>a<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u098f\u0995\u099f\u09be \u09b2\u09ae\u09cd\u09ac\u09be \u099a\u09cb\u0999 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995 \u09af\u09be\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf \u098f\u0995\u0995 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c \\lambda<\/span><\/span>\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, \u099a\u09cb\u0999\u09c7\u09b0 \u0985\u0995\u09cd\u09b7 \u09a5\u09c7\u0995\u09c7 <\/span>r<\/span><\/span> \u09a6\u09c2\u09b0\u09c7 \u09ac\u09b9\u09bf\u09b8\u09cd\u09a5 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09f0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\"\u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4<\/strong>\u099a\u09cb\u0999\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u09ae\u09be\u0995\u09cd\u09b7\u09c7 <\/span>r<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u098f\u09ac\u0982 <\/span>L<\/span><\/span> \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u099a\u09cb\u0999 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995\u0964 \u098f\u09ad\u09be\u09ac\u09c7 \u0997\u09a0\u09bf\u09a4 \u099a\u09cb\u0999\u0995\u09c7 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u099a\u09cb\u0999<\/strong> \u09ac\u09b2\u09c7\u0964 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u099a\u09cb\u0999\u099f\u09bf \u0996\u09c1\u09ac\u0987 \u09a6\u09c0\u09b0\u09cd\u0998 \u09ac\u09b2\u09c7 \u098f\u09b0 \u09a6\u09c1\u0987 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac \u0985\u0997\u09cd\u09b0\u09be\u09b9\u09cd\u09af \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09be\u09ae\u09cd\u09af \u0997\u09c1\u09a3\u09be\u09ac\u09b2\u09bf\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u099a\u09cb\u0999\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a4\u09cd\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>\\vec{E}<\/span><\/span>-\u098f\u09b0 \u09ae\u09be\u09a8 \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u09a6\u09bf\u0995 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7 \u09ac\u09bf\u09ac\u09c7\u099a\u09bf\u09a4 \u0995\u09cb\u09a8\u09cb \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 d \\vec{a}<\/span><\/span> -\u098f\u09b0 \u09a6\u09bf\u0995\u0993 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u09a4\u09b2 \u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 q= \\lambda L<\/span><\/span>\u00a0<\/span>\u09b9\u09ac\u09c7\u0964 \u098f\u0996\u09be\u09a8\u09c7 \\lambda<\/span><\/span>\u00a0<\/span>= \u09aa\u09cd\u09b0\u09a4\u09bf \u098f\u0995\u0995 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3\u0964<\/span><\/p>\n

\u098f\u0996\u09a8 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\oint_{s} \\vec{E} \\cdot d \\vec{a}=\\oint_{s} E d a \\frac{q}{\\epsilon_{o}}<\/span>\n

\u09ac\u09be,\u00a0 \u00a0 E(2 \\pi r L)=\\frac{\\lambda L}{\\epsilon_{o}}<\/span><\/span><\/p>\n

\u00a0 \u00a0\\therefore \\quad E=\\frac{\\lambda}{2 \\pi \\epsilon_{o} r}<\/span><\/span>\u00a0<\/span><\/p>\n

\u098f\u099f\u09bf\u0987 \u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u0964 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

\u00a0\\vec{E}=\\frac{\\lambda}{2 \\pi \\epsilon_{o}} \\frac{\\vec{r}}{r^{2}}<\/span><\/span><\/p>\n

(\u0997) \u0985\u09b8\u09c0\u09ae \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09b0\u09c7\u0996\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/b>(The electric field intensity for a charge line of infinite length)<\/b><\/h3>\n

\u09b8\u09c1\u09b7\u09ae\u09ad\u09be\u09ac\u09c7 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u0985\u09b8\u09c0\u09ae \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09a4\u09be\u09b0 \u0985\u09a5\u09ac\u09be \u099a\u09be\u09b0\u09cd\u099c \u09b0\u09c7\u0996\u09be \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995 \u09af\u09be\u09b0 \u099a\u09be\u09b0\u09cd\u099c \u0998\u09a8\u09a4\u09cd\u09ac \u09ac\u09be \u098f\u0995\u0995 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c \\lambda<\/span><\/span><\/p>\n

\"\u0985\u09b8\u09c0\u09ae<\/b>\u099a\u09be\u09b0\u09cd\u099c \u09b0\u09c7\u0996\u09be \u09b9\u09a4\u09c7 <\/span>r<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>P<\/span><\/span> \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 <\/span>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>E<\/span><\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u099a\u09be\u09b0\u09cd\u099c \u09b0\u09c7\u0996\u09be\u0995\u09c7 \u0985\u0995\u09cd\u09b7 \u0995\u09b0\u09c7 <\/span>l<\/span><\/span>\u00a0\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u098f\u09ac\u0982 <\/span>e<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u099a\u09cb\u0999 \u0995\u09b2\u09cd\u09aa\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09cb\u0999\u09c7\u09b0 \u09ac\u0995\u09cd\u09b0\u09a4\u09b2\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u0995\u09b0\u09ac\u09c7\u0964 \u098f\u0987 \u09ac\u0995\u09cd\u09b0\u09a4\u09b2\u09c7\u09b0 \u09b8\u0995\u09b2 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>\\vec{E}<\/span><\/span>–<\/span>\u098f\u09b0 \u09ae\u09be\u09a8 \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u09ac\u0995\u09cd\u09b0\u09a4\u09b2\u09c7\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0\u0964\u00a0<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>p<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>\\vec{E}<\/span><\/span> \u098f\u09ac\u0982 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 d \\vec{a}<\/span><\/span>\u00a0\u09b8\u09ae\u09ae\u09c1\u0996\u09c0\u0964 \u0995\u09be\u099c\u09c7\u0987 \u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\epsilon_{o} \\oint \\vec{E} \\cdot d \\vec{a}=\\epsilon_{o} \\oint E d a=\\lambda l<\/span>\n

\u09ac\u09be,\u00a0 \u00a0\\epsilon_{o} E(2 \\pi r l)=\\lambda l<\/span><\/span><\/p>\n\\therefore \\quad E=\\frac{\\lambda}{2 \\pi \\epsilon_{o} r}<\/span>\n

\u0997\u09be\u0989\u09b8\u09c0\u09af\u09bc \u099a\u09cb\u0999\u09c7\u09b0 \u09a6\u09c1\u0987 \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u09a4\u09b2\u09c7\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 E \u09b8\u09ae\u0995\u09cb\u09a3\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964 \u0995\u09be\u099c\u09c7\u0987, \u0989\u09ad\u09af\u09bc \u09ac\u0995\u09cd\u09b0\u09a4\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \\epsilon_{o} \\oint \\vec{E} \\cdot d \\vec{a}=0<\/span><\/span>\u0964 \u0985\u09a4\u098f\u09ac, \u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0,<\/span><\/p>\nE=\\frac{\\lambda}{2 \\pi \\epsilon_{o} r}<\/span>\n

(\u0998) \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09b8\u09ae\u09a4\u09b2 \u09aa\u09b0\u09bf\u09ac\u09be\u09b9\u09c0\u09b0 \u09b8\u09a8\u09cd\u09a8\u09bf\u0995\u099f\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/b>(The electric field is predominant near the charged plane conductor)<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>A B<\/span> <\/span>\u098f\u0995\u099f\u09bf \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09b8\u09ae\u09a4\u09b2 \u09aa\u09c3\u09b7\u09cd\u09a0\u0964 \u098f\u09b0 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a4\u09b2 \u0998\u09a8\u09a4\u09cd\u09ac \\sigma<\/span><\/span>\u0964 \u098f\u0987 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09a8\u09bf\u0995\u099f\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>E<\/span><\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\"\u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4<\/span>\u09b8\u09ae\u09a4\u09b2 \u09aa\u09c3\u09b7\u09cd\u09a0\u09c7\u09b0 \u0989\u09ad\u09af\u09bc \u09a6\u09bf\u0995\u09c7 \u09a6\u09c1\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 C<\/span> \u0993 D<\/span> \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09bf \u098f\u09ac\u0982 \u098f\u0987 \u09a6\u09c1\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 <\/span>d a<\/span><\/span> \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u099a\u09cb\u0999 \u0995\u09b2\u09cd\u09aa\u09a8\u09be \u0995\u09b0\u09bf\u0964 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u098f\u0996\u09a8 C<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <\/span>d a<\/span><\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0993\u09aa\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u0986\u09ac\u09c7\u09b6 \u09b9\u09ac\u09c7 <\/span>E d a<\/span><\/span> \u098f\u09ac\u0982 \u098f\u099f\u09be \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0\u0964 \u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 D<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <\/span>d a<\/span><\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0993\u09aa\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u0986\u09ac\u09c7\u09b6 <\/span>E d a<\/span><\/span> \u098f\u09ac\u0982 \u098f\u099f\u09be \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964 \u0986\u09ac\u09be\u09b0 \u099a\u09cb\u0999\u09c7\u09b0 \u09ac\u0995\u09cd\u09b0\u09aa\u09c3\u09b7\u09cd\u09a0\u09c7 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u0986\u09ac\u09c7\u09b6 \\int \\overrightarrow{E .} d \\vec{a}=<\/span><\/span>\u0964 \u0985\u09a4\u098f\u09ac \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u099a\u09cb\u0999\u09c7\u09b0 \u0993\u09aa\u09b0 \u09ae\u09cb\u099f \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u0986\u09ac\u09c7\u09b6 = <\/span>E d a+E d a=2 E d a<\/span> <\/span>\u098f\u09ac\u0982 \u098f\u09b0 \u09a6\u09bf\u0995 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0\u0964<\/span><\/p>\n

\u0997\u09be\u0989\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\oint \\vec{E} \\cdot d \\vec{a}=\\frac{q}{\\epsilon_{o}}<\/span>\n

E d a+E d a=\\frac{\\sigma d a}{\\epsilon_{o}} \\quad[\\therefore \\quad q=\\sigma d a]<\/span>\u00a0\u00a0<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ae\u09cb\u099f \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u0986\u09ac\u09c7\u09b6,<\/span><\/p>\n

2 E d a=\\frac{\\sigma d a}{2 \\epsilon_{o}}<\/span>\u00a0<\/span><\/p>\n

\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0986\u0995\u09be\u09b0\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\\vec{E}=\\frac{\\sigma}{2 \\epsilon_{o}} \\hat{n}<\/span>\u00a0 \u00a0\u00a0<\/span><\/p>\n

\u09af\u0996\u09a8 <\/span>\\hat{n}<\/span><\/span>\u00a0<\/span>\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b8\u09ae\u09a4\u09b2\u09c7\u09b0 \u0993\u09aa\u09b0 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c2\u0996\u09c0 \u09b2\u09ae\u09cd\u09ac \u098f\u0995\u0995 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0964 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09df \u09af\u09c7, \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09b8\u09ae\u09a4\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09dc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09a8\u09bf\u09b0\u09aa\u09c7\u0995\u09cd\u09b7 \u09b9\u09df\u0964<\/span><\/p>\n

(\u0999) \u09a6\u09c1\u099f\u09bf \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09aa\u09be\u09a4\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/b>(The electric field prevails due to two charged parallel sheets)<\/b><\/h3>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, M \u0993 N \u09a6\u09c1\u099f\u09bf \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09aa\u09b0\u09bf\u09ac\u09be\u09b9\u09c0 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 M \u09aa\u09be\u09a4 \u09a7\u09a8\u099a\u09be\u09b0\u09cd\u099c\u09c7 \u098f\u09ac\u0982 N \u09aa\u09be\u09a4 \u098b\u09a3\u099a\u09be\u09b0\u09cd\u099c\u09c7 \u098f\u0995\u0987 \u09a4\u09b2 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4\u0964 \u098f\u09a6\u09c7\u09b0 \u0989\u09ad\u09af\u09bc\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a4\u09b2 \u0998\u09a8\u09a4\u09cd\u09ac <\/span>\u0964 \u09aa\u09be\u09a4\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 P-\u098f\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 <\/span>\\vec{E}<\/span><\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\"\u09a6\u09c1\u099f\u09bf<\/b>\u098f\u0996\u09a8 <\/span>M <\/span>\u09aa\u09be\u09a4\u09c7\u09b0 \u099c\u09a8\u09cd\u09af <\/span>P <\/span>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b9\u09ac\u09c7 \\mathrm{E}_{1}=\\frac{\\sigma}{2 \\epsilon_{o}}<\/span><\/span>\u00a0\u098f\u09ac\u0982 \u098f\u09b0 \u09a6\u09bf\u0995 \u09b9\u09ac\u09c7 <\/span>MN <\/span>\u09ac\u09b0\u09be\u09ac\u09b0\u0964 \u0986\u09ac\u09be\u09b0<\/span> N <\/span>\u09aa\u09be\u09a4\u09c7\u09b0 \u099c\u09a8\u09cd\u09af <\/span>P <\/span>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 \\mathrm{E}_{2}=\\frac{\\sigma}{2 \\epsilon_{o}}<\/span><\/span>\u00a0\u09b9\u09ac\u09c7 \u098f\u09ac\u0982 <\/span>N <\/span>\u09aa\u09be\u09a4 \u098b\u09a3\u099a\u09be\u09b0\u09cd\u099c\u09c7 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09ac\u09b2\u09c7 E_{2}<\/span><\/span>–<\/span>\u098f\u09b0 \u09a6\u09bf\u0995 <\/span>MN <\/span>\u09ac\u09b0\u09be\u09ac\u09b0 \u09b9\u09ac\u09c7\u0964 \u0985\u09a4\u098f\u09ac<\/span>,<\/span> P <\/span>\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ae\u09cb\u099f \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b9\u09ac\u09c7<\/span>,<\/span><\/p>\n\\begin{aligned}\n\n& E=E_{1}+E_{2}=\\frac{\\sigma}{2 \\epsilon_{o}}+\\frac{\\sigma}{2 \\epsilon_{o}} \\\\\n\n\\therefore & E=\\frac{\\sigma}{\\epsilon_{o}}\n\n\\end{aligned}<\/span>\n

\u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995 \u09b9\u09ac\u09c7 <\/span>M <\/span>\u09aa\u09be\u09a4 \u09b9\u09a4\u09c7 <\/span>N <\/span>\u09aa\u09be\u09a4\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09a7\u09a8\u099a\u09be\u09b0\u09cd\u099c \u09b9\u09a4\u09c7 \u098b\u09a3\u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7\u0964<\/span> \u09aa\u09be\u09a4\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>Q-<\/span>\u09a4\u09c7 <\/span>M <\/span>\u0993 <\/span>N <\/span>\u09aa\u09be\u09a4\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 E_{1}=\\frac{\\sigma}{2 \\epsilon_{o}}<\/span><\/span>\u00a0\u098f\u09ac\u0982 E_{2}=\\frac{\\sigma}{2 \\epsilon_{o}}<\/span><\/span>\u00a0\u09b9\u09ac\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u098f\u09b0\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09a6\u09bf\u0995\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09be\u09af\u09bc \u09b2\u09ac\u09cd\u09a7\u09bf \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09ac\u09c7\u0964 \u098f\u09b0 \u0985\u09b0\u09cd\u09a5 \u09b9\u09b2\u09cb \u09aa\u09be\u09a4\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ac\u09be\u0987\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09a5\u09be\u0995\u09ac\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n

\u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09c0\u09ae\u09be\u09ac\u09a6\u09cd\u09a7\u09a4\u09be <\/b>(Limitations of Coulomb’s law)<\/b><\/h2>\n
    \n
  1. \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0995\u09c7\u09ac\u09b2\u09ae\u09be\u09a4\u09cd\u09b0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u09af\u09cb\u099c\u09cd\u09af; \u0985\u09a8\u09bf\u09af\u09bc\u09ae\u09bf\u09a4 \u0986\u0995\u09c3\u09a4\u09bf\u09b0 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u098f \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc \u09a8\u09be\u0964 \u0995\u09c7\u09a8\u09a8\u09be \u0993\u0987 \u09b8\u09ae\u09b8\u09cd\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b8\u09a0\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc \u09a8\u09be\u0964<\/span><\/li>\n
  2. \u00a0<\/span>\u099a\u09be\u09b0\u09cd\u099c\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1 \u09af\u09be\u09a6\u09c7\u09b0 \u0986\u0995\u09be\u09b0 \u098f\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u0985\u09a8\u09c7\u0995 \u099b\u09cb\u099f<\/span>, <\/span>\u09b8\u09c7\u0987 \u09b8\u09ae\u09b8\u09cd\u09a4 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/span> \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09af\u09cb\u099c\u09cd\u09af\u0964 \u099a\u09be\u09b0\u09cd\u099c\u09bf\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1 \u09ac\u09a1\u09bc \u09b9\u09b2\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09b2\u09c7\u09b0 \u0993\u09aa\u09b0 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac \u09aa\u09a1\u09bc\u09ac\u09c7\u0964<\/span><\/li>\n
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  5. \u09b8\u09a6\u09c3\u09b6 \u099a\u09be\u09b0\u09cd\u099c (\u09af\u09c7\u09ae\u09a8 \u0997\u09cb\u09b2\u09be\u0995\u09be\u09b0 \u099a\u09be\u09b0\u09cd\u099c) \u09ac\u09bf\u09a8\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09be \u09a6\u09c1\u09b0\u09c2\u09b9\u0964<\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    \u099c\u09be\u09b0\u09cd\u09ae\u09be\u09a8 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u0995\u09be\u09b0\u09cd\u09b2 \u09ab\u09cd\u09b0\u09c7\u09a1\u09b0\u09bf\u0995 \u0997\u09be\u0989\u09b8 (Carl Friedrich Gauss) \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8 \u0993 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u098f\u0995\u099f\u09bf \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a6\u09be\u09a8 \u0995\u09b0\u09c7\u09a8\u0964 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ac\u09a6\u09cd\u09a7 \u09a4\u09b2\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09ac\u09be\u09b2\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u098f \u09b8\u09c2\u09a4\u09cd\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09c3\u09a4 \u09b9\u09af\u09bc\u0964 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09ac\u09bf\u09ac\u09c3\u09a4 \u0995\u09b0\u09be\u09b0 \u0986\u0997\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ab\u09cd\u09b2\u09be\u0995\u09cd\u09b8, \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0<\/p>\n

    Read More<\/a><\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4246,3029,50,51],"tags":[1991,1992,1990,1993],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2698"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=2698"}],"version-history":[{"count":9,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2698\/revisions"}],"predecessor-version":[{"id":4374,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2698\/revisions\/4374"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}