{"id":2639,"date":"2022-03-24T11:47:22","date_gmt":"2022-03-24T11:47:22","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2639"},"modified":"2023-06-26T16:41:18","modified_gmt":"2023-06-26T10:41:18","slug":"electric-dipole","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/electric-dipole\/","title":{"rendered":"\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 (Electric dipole)"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">\u09b8\u09ae\u09aa\u09b0\u09bf\u09ae\u09be\u09a3\u09c7\u09b0 \u09a6\u09c1\u099f\u09bf \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09a7\u09b0\u09cd\u09ae\u09c0 \u09a4\u09a1\u09bc\u09bf\u09ce \u099a\u09be\u09b0\u09cd\u099c \u0996\u09c1\u09ac \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u0997\u09a0\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09b2\u09ae\u09cd\u09ac-\u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995 \u09b0\u09c7\u0996\u09be\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u098f\u0987 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c\u0995\u09c7 \u09b8\u09b0\u09be\u09a4\u09c7 \u09b8\u09ae\u09cd\u09aa\u09be\u09a6\u09bf\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<p><b>\u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09a7\u09b0\u09cd\u09ae\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09be\u09b0\u09cd\u099c \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u0996\u09c1\u09ac \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a5\u09be\u0995\u09b2\u09c7 \u09a4\u09be\u0995\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ac\u09b2\u09c7\u0964<\/b><\/p>\n<p><span style=\"font-weight: 400;\">\u0989\u09a6\u09be\u09b9\u09b0\u09a3\u09b8\u09cd\u09ac\u09b0\u09c2\u09aa \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u09b9\u09be\u0987\u09a1\u09cd\u09b0\u09cb\u099c\u09c7\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf \u09a7\u09a8 \u09aa\u09cd\u09b0\u09cb\u099f\u09a8 \u098f\u09ac\u0982 \u098f\u0995\u099f\u09bf \u098b\u09a3 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u0986\u099b\u09c7\u0964 \u0985\u09a4\u098f\u09ac \u0987\u09b9\u09be \u098f\u0995\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u0964 \u09aa\u09be\u09a8\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\mathrm{H}_{2} \\mathrm{O}\\right)<\/span><\/span><span style=\"font-weight: 400;\">, \u0995\u09cd\u09b2\u09cb\u09b0\u09cb\u09ab\u09b0\u09ae <span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\mathrm{CHCl}_{3}\\right)<\/span><\/span><span style=\"font-weight: 400;\">, \u0985\u09cd\u09af\u09be\u09ae\u09cb\u09a8\u09bf\u09af\u09bc\u09be <span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\mathrm{NH}_{3}\\right)<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09b2\u09cb \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0989\u09a6\u09be\u09b9\u09b0\u09a3\u0964 \u098f\u09b8\u09ac \u0985\u09a3\u09c1\u09a4\u09c7 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0993 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u0986\u09a7\u09be\u09a8 \u09ac\u09a3\u09cd\u099f\u09a8\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u0996\u09a8\u0993 \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b9\u09af\u09bc \u09a8\u09be\u0964<\/span><\/p>\n<h2><b>\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/b><\/h2>\n<p><span style=\"font-weight: 400;\"><strong>\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf\u09b0 \u0986\u09a7\u09be\u09a8\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u098f\u09ac\u0982 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u0995\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u09ac\u09b2\u09c7\u0964<\/strong> \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u098f\u0995\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf\u09b0 \u0986\u09a7\u09be\u09a8\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 <span class=\"katex-eq\" data-katex-display=\"false\">= \\text {q}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span><span style=\"font-weight: 400;\">=<span class=\"katex-eq\" data-katex-display=\"false\">\\text {2 l}<\/span><\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span><span style=\"font-weight: 400;\"> \u00a0 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">p=q \\times 2 l<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09c2\u09aa \u09b9\u09b2\u09cb <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{p}=2 q \\vec{l} \\mid<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0964 \u098f\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u098b\u09a3 \u099a\u09be\u09b0\u09cd\u099c \u09b9\u09a4\u09c7 \u09a7\u09a8 \u099a\u09be\u09b0\u09cd\u099c\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7\u0964<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b2\u09ae\u09cd\u09ac-\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cb\u09a8\u09cb \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c\u0995\u09c7 \u09b8\u09b0\u09be\u09b2\u09c7 \u0995\u09cb\u09a8\u09cb \u0995\u09be\u099c \u09b8\u09ae\u09cd\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc \u09a8\u09be \u0995\u09c7\u09a8?<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09b2\u09ae\u09cd\u09ac-\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995 \u09b0\u09c7\u0996\u09be\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09c7\u09be \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u098f\u0987 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c\u0995\u09c7 \u09b8\u09b0\u09be\u09a4\u09c7 \u09b8\u09ae\u09cd\u09aa\u09be\u09a6\u09bf\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09cb\u09a8\u09cb \u0995\u09be\u099c \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc \u09a8\u09be\u0964<\/span><\/p>\n<h2><b>\u09b8\u09c1\u09b7\u09ae \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u099f\u09b0\u09cd\u0995 <\/b><b>(Torque on a dipole in a uniform electric field)<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">+ \\text {q}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <span class=\"katex-eq\" data-katex-display=\"false\">- \\text {q}<\/span><\/span><span style=\"font-weight: 400;\"> \u0986\u09a7\u09be\u09a8\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 <span class=\"katex-eq\" data-katex-display=\"false\">\\text {A B}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b8\u09c1\u09b7\u09ae \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4\u0964 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text {A B}<\/span> = <span class=\"katex-eq\" data-katex-display=\"false\">\\text {2 l}<\/span><\/span><span style=\"font-weight: 400;\"> \u09a7\u09b0\u09bf, \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 <\/span><span style=\"font-weight: 400;\"> \u0995\u09cb\u09a3\u09c7 \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 B \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">+ \\text {q}<\/span><\/span><span style=\"font-weight: 400;\"> \u0986\u09a7\u09be\u09a8\u09c7\u09b0 \u0993\u09aa\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">+ \\text {q E}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995 \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964 \u09aa\u0995\u09cd\u09b7\u09be\u09a8\u09cd\u09a4\u09b0\u09c7 A \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">- \\text {q}<\/span><\/span><span style=\"font-weight: 400;\"> \u0986\u09a7\u09be\u09a8\u09c7\u09b0 \u0993\u09aa\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">- \\text {q E}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09a6\u09bf\u0995\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a6\u09c1\u099f\u09bf \u09b8\u09ae\u09be\u09a8, \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964 \u09a4\u09be\u0987 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09b2\u09a6\u09cd\u09a7\u09bf \u09ac\u09b2 \u09b6\u09c2\u09a8\u09cd\u09af\u0964 \u09a4\u09ac\u09c7 \u09ac\u09b2 \u09a6\u09c1\u099f\u09bf \u098f\u0995\u0987 \u09b0\u09c7\u0996\u09be\u09af\u09bc \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09a8\u09be \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u098f\u09b0\u09be \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u099f\u09b0\u09cd\u0995 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09c7\u0964 \u098f\u0987 \u099f\u09b0\u09cd\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b9\u09ac\u09c7\u2014\u00a0<\/span><\/p>\n<p><b><img loading=\"lazy\" class=\"aligncenter wp-image-2740 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/11\/2.13-1024x646.png\" alt=\"\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u099f\u09b0\u09cd\u0995\" width=\"1024\" height=\"646\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.13-1024x646.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.13-300x189.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.13-768x485.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.13.png 1054w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/b><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tau=<\/span> <\/span><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2\u09c7\u09b0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ae\u09be\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">\\times<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09b2\u09ae\u09cd\u09ac<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\tau=q E \\times 2 l \\sin \\theta=p E \\sin \\theta<\/span>\u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">[\\because \\quad p=2 q l]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u099a\u09cd\u099b\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u0995\u09c7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09b0\u09c2\u09aa\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc\u2014\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{\\tau}=\\vec{p} \\times \\vec{E}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u099f\u09bf\u0987 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u099f\u09b0\u09cd\u0995\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u0993 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(i) \u09af\u0996\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=90^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u00a0<\/span><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">\\tau=p E \\sin 90^{\\circ}=p E<\/span><\/span><span style=\"font-weight: 400;\">,\u00a0<\/span><span style=\"font-weight: 400;\">\u09a4\u0996\u09a8 \u099f\u09b0\u09cd\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09b9\u09af\u09bc, \u0985\u09a4\u098f\u09ac <span class=\"katex-eq\" data-katex-display=\"false\">\\tau_{\\max }=p E<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(ii) \u09af\u0996\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=0^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"> \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tau=p E \\sin 0^{\\circ}=0<\/span>, <\/span><span style=\"font-weight: 400;\">\u09a4\u0996\u09a8 \u099f\u09b0\u09cd\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">\\tau_{\\max }=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\n<h2><b>\u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u0995\u09c7 \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u0995\u09b0\u09a4\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c\u00a0 <\/b><b>(Work done to deflect a dipole in an electric field)<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be\u09a7\u09be\u09b9\u09c0\u09a8\u09ad\u09be\u09ac\u09c7 \u098f\u0995\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u0995\u09cb\u09a8\u09cb \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a5\u09be\u0995\u09b2\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u098f\u0987 \u09b8\u09be\u09ae\u09cd\u09af \u0985\u09ac\u09b8\u09cd\u09a5\u09be \u09a5\u09c7\u0995\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u0995\u09b0\u09a4\u09c7 \u09b9\u09b2\u09c7 \u098f\u09b0 \u0993\u09aa\u09b0 \u0995\u09be\u099c \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc\u0964 \u098f\u0987 \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09a4\u09c7 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09b0\u09c2\u09aa\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09a5\u09be\u0995\u09c7\u0964<\/span><\/p>\n<p><strong><img loading=\"lazy\" class=\"aligncenter wp-image-2741 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/11\/2.14-1024x646.png\" alt=\"\u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u0995\u09c7 \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u0995\u09b0\u09a4\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c\" width=\"1024\" height=\"646\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.14-1024x646.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.14-300x189.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.14-768x485.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.14.png 1054w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/strong><span style=\"font-weight: 400;\">\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0998\u09c2\u09b0\u09cd\u09a3\u09a8\u09c7\u09b0 \u09b8\u09ae\u09af\u09bc \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ae\u09c1\u09b9\u09c1\u09b0\u09cd\u09a4\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> <\/span><span style=\"font-weight: 400;\">\u0995\u09cb\u09a3\u09c7 \u0986\u09a8\u09a4 \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u098f\u0987 \u09b8\u09ae\u09af\u09bc \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0993\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u099f\u09b0\u09cd\u0995, <span class=\"katex-eq\" data-katex-display=\"false\">\\tau=p E \\sin \\theta<\/span><\/span>\u00a0\u0964<span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf\u0995\u09c7 \u0985\u09a4\u09bf\u09b0\u09bf\u0995\u09cd\u09a4 <\/span><span style=\"font-weight: 400;\">d\u03b8<\/span><span style=\"font-weight: 400;\"> \u0995\u09cb\u09a3\u09c7 \u09b8\u09b0\u09a3 \u0998\u099f\u09be\u09a4\u09c7 \u09b9\u09b2\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c,\u00a0<\/span><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">d W=\\tau d \\theta=p E \\sin \\theta d \\theta<\/span> <span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span>\u00a0<\/span><span style=\"font-weight: 400;\"> \u0995\u09cb\u09a3\u09c7 \u0998\u09c1\u09b0\u09be\u09a4\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c,\u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">W=p E \\int_{0}^{\\alpha} \\sin \\theta d \\theta=p E(1-\\cos \\alpha)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u098f\u0987 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf,\u00a0<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">U=p E(1-\\cos \\alpha)<\/span>\n<p><span style=\"font-weight: 400;\">(i) \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=90^{\\circ}<\/span> <\/span><span style=\"font-weight: 400;\">\u0995\u09cb\u09a3\u09c7 \u0998\u09c1\u09b0\u09be\u09a4\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">W=p E\\left(1-\\cos 90^{\\circ}\\right)=p E<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">(ii) \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u099f\u09bf\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=180^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0995\u09cb\u09a3\u09c7 \u0998\u09c1\u09b0\u09be\u09a4\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c,\u00a0<\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">W=p E\\left(1-\\cos 180^{\\circ}\\right)=p E(1+1)=2 p E<\/span><\/span><\/p>\n<h2><b>\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09bf\u09ad\u09ac\u00a0 <\/b><b>(Electric potential due to electric dipole)<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">+q<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">-q<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09be\u09b0\u09cd\u099c\u0964 \u098f\u09b0\u09be \u09b6\u09c2\u09a8\u09cd\u09af \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">B<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">2 l<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u09a5\u09c7\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09c7\u099b\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u09a7\u09b0\u09bf <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">B<\/span><span style=\"font-weight: 400;\">-\u098f\u09b0 \u09ae\u09a7\u09cd\u09af-\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\">\u0964 \u098f\u0996\u09a8 <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>\u00a0<\/span><span style=\"font-weight: 400;\"> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a8\u09c7\u0987\u0964 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u09a7\u09b0\u09bf <\/span><span style=\"font-weight: 400;\">OP =<span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>,<\/span> <span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\angle POA = \\theta<\/span><\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P O<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P O<\/span><\/span><span style=\"font-weight: 400;\">-\u098f\u09b0 \u09ac\u09b0\u09cd\u09a7\u09bf\u09a4 \u0985\u0982\u09b6\u09c7\u09b0 \u0993\u09aa\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">A N^{\\prime}<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">B N<\/span><\/span><span style=\"font-weight: 400;\"> \u09b2\u09ae\u09cd\u09ac\u0964<\/span><\/p>\n<p><strong><img loading=\"lazy\" class=\"aligncenter wp-image-2742 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/11\/2.15-1024x894.png\" alt=\"\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09bf\u09ad\u09ac\u00a0\" width=\"1024\" height=\"894\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.15-1024x894.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.15-300x262.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.15-768x670.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.15.png 1054w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/> <\/strong><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{l}\n\n\\therefore P \\text { \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac, } V_{p}=\\frac{1}{4 \\pi \\epsilon_{o}}\\left\\{\\frac{q}{A P}+\\left(-\\frac{q}{B P}\\right)\\right\\} \\\\\n\nV_{p}=\\frac{1}{4 \\pi \\epsilon_{o}}\\left(\\frac{q}{A P}-\\frac{q}{B P}\\right) \\\\\n\nP N=B P=r+l \\cos \\theta=r_{2} \\\\\n\n\\therefore \\text { \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (2.36) \u09b9\u09a4\u09c7 \u09aa\u09be\u0987 }\n\n\\end{array}<\/span> <span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\nV_{p} &amp;=\\frac{1}{4 \\pi \\epsilon_{o}}\\left\\{\\frac{q}{r_{1}}-\\frac{q}{r_{2}}\\right\\} \\\\\n\n&amp;=\\frac{1}{4 \\pi \\epsilon_{o}}\\left\\{\\frac{q}{r-l \\cos \\theta}-\\frac{q}{r+l \\cos \\theta}\\right\\} \\\\\n\n&amp;=\\frac{1}{4 \\pi \\epsilon_{o}}\\left\\{\\frac{q(r+l \\cos \\theta)-q(r-l \\cos \\theta)}{r^{2}-l^{2} \\cos ^{2} \\theta}\\right\\} \\\\\n\n&amp;=\\frac{1}{4 \\pi \\epsilon_{o}}\\left\\{\\frac{q(r+l \\cos \\theta-r+l \\cos \\theta)}{r^{2}-l^{2} \\cos ^{2} \\theta}\\right\\}=\\frac{1}{4 \\pi \\epsilon_{o}}\\left\\{\\frac{q \\times 2 l \\cos \\theta}{r^{2}-l^{2} \\cos ^{2} \\theta}\\right\\}\n\n\\end{aligned}<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">r \\gg l<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u0993\u09df\u09be\u09df <span class=\"katex-eq\" data-katex-display=\"false\">l^{2} \\cos ^{2} \\theta<\/span><\/span>\u00a0<span style=\"font-weight: 400;\">\u0995\u09c7 \u0989\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09b0\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\n\\therefore P \\text { \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac, } \\mathrm{V}_{p} &amp;=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{q \\times 2 l \\cos \\theta}{r^{2}} \\\\\n\n\\text { \u09ac\u09be, } \\mathrm{V}_{p} &amp;=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\cos \\theta}{r^{2}}\n\n\\end{aligned}<\/span>\n<p>\u098f\u0996\u09be\u09a8\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">q \\times 2 l=p=<\/span> \u09a6\u09cd\u09ac\u09bf\u09b0\u09cd\u09ae\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{V}_{p}=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\cos \\theta}{r^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u099f\u09bf\u0987 \u09b9\u09b2\u09cb \u09a4\u09dc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c2\u09b0 \u099c\u09a8\u09cd\u09af \u09ac\u09bf\u09ad\u09ac\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be\u0964<\/span><\/p>\n<p><b>\u09a6\u09cd\u09b0\u09b7\u09cd\u099f\u09ac\u09cd\u09af (Note):<\/b><\/p>\n<p><span style=\"font-weight: 400;\">(i) \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09df, \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a4\u09dc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u09cd\u09a5\u09be\u09aa\u09bf\u09a4 \u09b9\u09df, \u09a4\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{V}_{p}=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p}{r^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">(ii) \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=90^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09df, \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a4\u09dc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0993\u09aa\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u09b9\u09df, \u09a4\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{V}_{p}=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><i><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09b2\u09ae\u09cd\u09ac<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a8\u09cd\u09a1\u0995\u09c7\u09b0<\/span><\/i> <i><span style=\"font-weight: 400;\">\u0993\u09aa\u09b0<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09af\u09c7<\/span><\/i> <i><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09a4\u09dc\u09bf\u09ce<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09ac\u09bf\u09ad\u09ac<\/span><\/i> <i><span style=\"font-weight: 400;\">\u09b6\u09c2\u09a8\u09cd\u09af\u0964<\/span><\/i><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(iii) \u0985\u09a8\u09cd\u09af \u0995\u09cb\u09a8\u09cb \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{V}_{p}=\\frac{1}{4 \\pi \\epsilon_{o} k} \\times \\frac{p \\cos \\theta}{r^{2}}<\/span><\/span><\/p>\n<h2><b>\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0<\/b> <b>\u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <\/b><b>(Electric field intensity due to electric dipole)<\/b><\/h2>\n<p><strong>\u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af (Electric field intensity): \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09ac\u09bf\u09ad\u09ac \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u09b9\u09be\u09b0\u0995\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09ac\u09b2\u09c7<\/strong><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af, <span class=\"katex-eq\" data-katex-display=\"false\">E=-\\frac{d V}{d r}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><strong><img loading=\"lazy\" class=\"aligncenter wp-image-2743 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/11\/2.16-1024x861.png\" alt=\"\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\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\" width=\"1024\" height=\"861\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.16-1024x861.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.16-300x252.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.16-768x646.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/11\/2.16.png 1054w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/strong><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 <\/span><span style=\"font-weight: 400;\">OP<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b0\u09be\u09ac\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af\u09c7\u09b0 \u0989\u09aa\u09be\u0982\u09b6\u09c7\u09b0 \u09a8\u09be\u09ae <strong>\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09ae\u09c1\u0996\u09c0 \u0989\u09aa\u09be\u0982\u09b6 (radial component)<\/strong>\u0964 \u098f\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">E_{r}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09af\u09bc [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\n\\therefore E_{r} &amp;=-\\frac{d}{d r}\\left(\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\cos \\theta}{r^{2}}\\right) \\\\\n\n&amp;=-\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{d}{d r}\\left(\\frac{p \\cos \\theta}{r^{2}}\\right)=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{2 p \\cos \\theta}{r^{3}}\n\n\\end{aligned}<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore<\/span><\/span><span style=\"font-weight: 400;\"> \u00a0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09bf\u09ad\u09ac <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p}{r^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0, <\/span><span style=\"font-weight: 400;\">OP<\/span><span style=\"font-weight: 400;\">-\u098f\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af\u09c7\u09b0 \u0989\u09aa\u09be\u0982\u09b6\u09c7\u09b0 \u09a8\u09be\u09ae \u09a4\u09bf\u09b0\u09cd\u09af\u0995 \u0989\u09aa\u09be\u0982\u09b6 (tangential component)\u0964 \u098f\u0995\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{\\theta}<\/span><\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u0986\u09ac\u09be\u09b0, \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <span class=\"katex-eq\" data-katex-display=\"false\">r d \\theta<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0964<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\n\\therefore E_{\\theta} &amp;=-\\frac{d V}{r d \\theta}=-\\frac{1}{r} \\cdot \\frac{d}{d \\theta}\\left(\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\cos \\theta}{r^{2}}\\right) \\\\\n\n&amp;=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\sin \\theta}{r^{3}}\n\n\\end{aligned}<\/span>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">= E<\/span><\/span><span style=\"font-weight: 400;\">\u0964 \u09a4\u09be \u09b9\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">E<\/span> <\/span><span style=\"font-weight: 400;\">\u09b9\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">E_{r}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0993 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{\\theta}<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u0964<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\n\\therefore \\quad E &amp;=\\sqrt{E_{r}^{2}+E_{\\theta}^{2}} \\\\\n\n&amp;=\\sqrt{\\left(\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{2 p \\cos \\theta}{r^{3}}\\right)^{2}+\\left(\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\sin \\theta}{r^{3}}\\right)^{2}} \\\\\n\n&amp;=\\frac{1}{4 \\pi \\epsilon_{o}} \\cdot \\frac{p}{r^{3}} \\sqrt{\\left(4 \\cos ^{2} \\theta+\\sin ^{2} \\theta\\right)} \\\\\n\n&amp;=\\frac{1}{4 \\pi \\epsilon_{o}} \\cdot \\frac{p}{r^{3}} \\sqrt{\\left(1+3 \\cos ^{2} \\theta\\right)}\n\n\\end{aligned}<\/span>\n<p><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">E<\/span><\/span><span style=\"font-weight: 400;\"> -\u098f\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\">\u00a0<span class=\"katex-eq\" data-katex-display=\"false\">E_{r}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09b0 \u09b8\u09be\u09a5\u09c7\u00a0 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">E<\/span> <\/span><span style=\"font-weight: 400;\">-\u098f\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">\\varphi<\/span>\u00a0<\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7\u00a0<\/span><\/p>\n<p><span style=\"background-color: var(--global--color-background); color: var(--global--color-primary); font-family: var(--global--font-secondary); font-size: var(--global--font-size-base);\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\n\\tan \\varphi &amp;=\\frac{E_{\\theta}}{E_{r}}=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p \\sin \\theta}{r^{3}} \/ \\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{2 p \\cos \\theta}{r^{3}} \\\\\n\n&amp;=\\frac{\\sin \\theta}{2 \\cos \\theta}=\\frac{1}{2} \\tan \\theta\n\n\\end{aligned}<\/span> <\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<h3><b>\u09ac\u09bf\u09b6\u09c7\u09b7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 (Special case) :<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u09e7. \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u09af\u09a6\u09bf \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0993\u09aa\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta=0^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09ac\u09c7\u0964 \u09b8\u09c7\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">E=\\frac{1}{4 \\pi \\epsilon_{0}} \\times \\frac{2 p}{r^{3}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09e8. \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u09af\u09a6\u09bf \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u09c7\u09b0 \u0993\u09aa\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta=90^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09ac\u09c7\u0964 \u09b8\u09c7\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">E=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p}{r^{3}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09e9. <span class=\"katex-eq\" data-katex-display=\"false\">0^{\\circ}&lt;\\theta&lt;90^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">,\u00a0<\/span><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u09af\u09a6\u09bf \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995\u09c7\u09b0 \u09a1\u09be\u09a8 \u09aa\u09be\u09b6\u09c7 \u09a4\u09a5\u09be \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c \u09af\u09c7 \u09aa\u09be\u09b6\u09c7 \u09b8\u09c7\u0987 \u09aa\u09be\u09b6\u09c7 \u09b9\u09af\u09bc \u09a4\u09be\u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\cos \\theta=+v e<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 \u09ac\u09bf\u09ad\u09ac \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ea. <span class=\"katex-eq\" data-katex-display=\"false\">90^{\\circ}&lt;\\theta&lt;180^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">,\u00a0<\/span><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u09af\u09a6\u09bf \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995\u09c7\u09b0 \u09ac\u09be\u09ae \u09aa\u09be\u09b6\u09c7 \u09a4\u09a5\u09be \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c \u09af\u09c7 \u09aa\u09be\u09b6\u09c7 \u09b8\u09c7\u0987 \u09aa\u09be\u09b6\u09c7 \u09b9\u09af\u09bc \u09a4\u09be\u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\cos \\theta=-v e<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 \u09ac\u09bf\u09ad\u09ac <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">V<\/span><\/span><span style=\"font-weight: 400;\"> \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09eb. <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=180^{\\circ}<\/span><\/span><span style=\"font-weight: 400;\">,\u00a0<\/span><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf \u09af\u09a6\u09bf \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0993\u09aa\u09b0 \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c \u09af\u09c7 \u09aa\u09be\u09b6\u09c7 \u09b8\u09c7\u0987 \u09aa\u09be\u09b6\u09c7 \u09b9\u09af\u09bc \u09a4\u09be\u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\cos 180^{\\circ}=-1 \\text { \u098f\u09ac\u0982 } \\mathrm{V}=\\frac{1}{4 \\pi \\epsilon_{0}} \\times \\frac{p}{r^{2}} \\text { \u09b9\u09ac\u09c7 }<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09cb \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u0998\u09a8\u09ab\u09b2\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u0986\u09b0 \u09ac\u09bf\u09ad\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/span><\/p>\n<ul>\n<li><b>\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09b8\u09cd\u09a5\u09bf\u09a4 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u09ac\u0982 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995\u09c7\u09b0 \u0993\u09aa\u09b0 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09bf\u09ad\u09ac \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af \u0995\u09a4 \u09b9\u09ac\u09c7?<\/b><b>\u00a0<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span><span style=\"font-weight: 400;\"> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09bf\u09ad\u09ac, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{V}_{p}=\\frac{1}{4 \\pi \\epsilon_{o}} \\times \\frac{p}{x^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{E}_{p}=\\frac{1}{4 \\pi \\varepsilon_{o}} \\frac{2 p}{x^{3}}<\/span><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u09c7\u09b0 \u0993\u09aa\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span><span style=\"font-weight: 400;\"> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7, <\/span><span style=\"font-weight: 400;\">\u09af\u0996\u09a8<\/span> <span style=\"font-weight: 400;\">\u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1<\/span> <span style=\"font-weight: 400;\">\u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/span> <span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">p=q \\times 2 l<\/span>, \u09a4\u0996\u09a8<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09bf\u09ad\u09ac<\/span><span style=\"font-weight: 400;\">,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{V}_{p}=0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09cd\u09b0\u09be\u09ac\u09b2\u09cd\u09af<\/span><span style=\"font-weight: 400;\">,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{E}_{p}=\\frac{1}{4 \\pi \\varepsilon_{o}} \\frac{2 p}{x^{3}}<\/span><\/p>\n<h2><b>\u0985\u09aa\u09b0\u09bf\u09ac\u09be\u09b9\u09c0 \u09ac\u09be \u0985\u09a8\u09cd\u09a4\u09b0\u0995 <\/b><b>(Insulator)<\/b><\/h2>\n<p><strong>\u09af\u09c7 \u09b8\u0995\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ae\u09c1\u0995\u09cd\u09a4 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u09a5\u09be\u0995\u09c7 \u09a8\u09be \u098f\u09ac\u0982 \u09af\u09c7 \u09b8\u0995\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5 \u09a4\u09a1\u09bc\u09bf\u09ce \u09aa\u09b0\u09bf\u09ac\u09b9\u09a8 \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be, <\/strong><span style=\"font-weight: 400;\"><strong>\u09a4\u09be\u09a6\u09c7\u09b0\u0995\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u0995 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5 \u09ac\u09b2\u09c7<\/strong>\u0964 <\/span><span style=\"font-weight: 400;\">\u09af\u09c7\u09ae\u09a8 \u0995\u09be\u0981\u099a<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">\u09b0\u09ac\u09be\u09b0<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b2\u09be\u09b8\u09cd\u099f\u09bf\u0995<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u09cb\u09a8\u09be\u0987\u099f \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09b8\u09ae\u09aa\u09b0\u09bf\u09ae\u09be\u09a3\u09c7\u09b0 \u09a6\u09c1\u099f\u09bf \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09a7\u09b0\u09cd\u09ae\u09c0 \u09a4\u09a1\u09bc\u09bf\u09ce \u099a\u09be\u09b0\u09cd\u099c \u0996\u09c1\u09ac \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09c7 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1 \u0997\u09a0\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u09a4\u09a1\u09bc\u09bf\u09ce \u09a6\u09cd\u09ac\u09bf\u09ae\u09c7\u09b0\u09c1\u09b0 \u09b2\u09ae\u09cd\u09ac-\u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995 \u09b0\u09c7\u0996\u09be\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u098f\u0987 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09be\u09b0\u09cd\u099c\u0995\u09c7 \u09b8\u09b0\u09be\u09a4\u09c7 \u09b8\u09ae\u09cd\u09aa\u09be\u09a6\u09bf\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc\u0964 \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09a7\u09b0\u09cd\u09ae\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/electric-dipole\/\">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":[3107,3104,3105,3106],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2639"}],"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=2639"}],"version-history":[{"count":11,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2639\/revisions"}],"predecessor-version":[{"id":6911,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2639\/revisions\/6911"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}