{"id":330724,"date":"2023-01-06T01:32:23","date_gmt":"2023-01-05T20:02:23","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/an-infinitely-long-uniform-line-charge-distribution-of-charge-per-unit-length-%ce%bb-lies-parallel-to-the-y-axis-in-the-y-z-plane-at-z32a-see-figure-if-the-magnitude-of-the-fl\/"},"modified":"2025-06-26T18:03:28","modified_gmt":"2025-06-26T12:33:28","slug":"an-infinitely-long-uniform-line-charge-distribution-of-charge-per-unit-length-%ce%bb-lies-parallel-to-the-y-axis-in-the-y-z-plane-at-z32a-see-figure-if-the-magnitude-of-the-fl","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-infinitely-long-uniform-line-charge-distribution-of-charg\/","title":{"rendered":"An infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \u00a0z=\u03bbLn\u03b50\u00a0(\u00a0\u03b50\u00a0=permittivity of free space), then the value of n \u00a0is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"An infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \u00a0z=\u03bbLn\u03b50\u00a0(\u00a0\u03b50\u00a0=permittivity of free space), then the value of n \u00a0is","custom_permalink":"question\/physics\/an-infinitely-long-uniform-line-charge-distribution-of-charg\/"},"categories":[],"acf":{"question":"

An infinitely long uniform line charge distribution of charge per unit length \u03bb<\/mi><\/math> lies parallel to the y-axis in the y-z plane at z<\/mi>=<\/mo>3<\/mn><\/msqrt>2<\/mn><\/mfrac>a<\/mi><\/math>  (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is  z<\/mi>=<\/mo>\u03bb<\/mi>L<\/mi><\/mrow>n<\/mi>\u03b5<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac><\/math> ( \u03b5<\/mi>0<\/mn><\/msub><\/math> =permittivity of free space), then the value of n<\/i>  is<\/p>
<\/figure>","options":null,"solution":"
<\/figure>

Imagine , a cylindrical gaussian surface of length L and radius a.<\/p>

tan<\/mi>\u2220<\/mo>A<\/mi>P<\/mi>O<\/mi><\/mrow><\/mfenced>=<\/mo>a<\/mi>2<\/mn><\/mfrac>3<\/mn><\/msqrt>a<\/mi><\/mrow>2<\/mn><\/mfrac><\/mfrac>=<\/mo>1<\/mn>3<\/mn><\/msqrt><\/mfrac>\u200b<\/mtext><\/mtd><\/mtr>\u21d2<\/mo>\u2220<\/mo>A<\/mi>P<\/mi>O<\/mi>=<\/mo>30<\/mn>0<\/mn><\/msup><\/mtd><\/mtr>\u200b<\/mtext>N<\/mi>o<\/mi>w<\/mi> <\/mo>,<\/mo> <\/mo>\u2220<\/mo>A<\/mi>P<\/mi>D<\/mi>=<\/mo>2<\/mn>\u2220<\/mo>A<\/mi>P<\/mi>O<\/mi>=<\/mo>60<\/mn>0<\/mn><\/msup><\/mtd><\/mtr><\/mtable><\/math><\/p>

Given rectangular surface ABCD subscribes an angle  60<\/mn>0<\/mn><\/msup><\/math> at the infinity long uniform line of charge.<\/p>

The total angle subscribe by cylinder is 360<\/mn>0<\/mn><\/msup><\/math> and charge enclosed is \u03bb<\/mi>L<\/mi><\/math>.<\/p>

Flux through the rectangle is same as the flux through <\/span>1<\/mn>6<\/mn><\/mfrac>t<\/mi>h<\/mi><\/mrow><\/msup><\/math> of the hexagon since it subtends <\/span>60<\/mn>0<\/mn><\/msup><\/math> at P and field lines are symmetrically radially outwards.<\/span><\/p>

\u03d5<\/mi>c<\/mi>y<\/mi>l<\/mi><\/mrow><\/msub>=<\/mo>q<\/mi>\u2208<\/mo>0<\/mn><\/msub><\/mfrac>\u200b<\/mtext><\/mtd><\/mtr>\u2234<\/mo>\u03d5<\/mi>A<\/mi>B<\/mi>C<\/mi>D<\/mi><\/mrow><\/msub>=<\/mo>q<\/mi>6<\/mn>\u2208<\/mo>0<\/mn><\/msub><\/mrow><\/mfrac>=<\/mo>\u03bb<\/mi>L<\/mi><\/mrow>6<\/mn>\u2208<\/mo>0<\/mn><\/msub><\/mrow><\/mfrac>\u200b<\/mtext><\/mtd><\/mtr>\u21d2<\/mo>n<\/mi>=<\/mo>6<\/mn><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"\nAn infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \u00a0z=\u03bbLn\u03b50\u00a0(\u00a0\u03b50\u00a0=permittivity of free space), then the value of n \u00a0is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"An infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \u00a0z=\u03bbLn\u03b50\u00a0(\u00a0\u03b50\u00a0=permittivity of free space), then the value of n \u00a0is\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-infinitely-long-uniform-line-charge-distribution-of-charg\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \u00a0z=\u03bbLn\u03b50\u00a0(\u00a0\u03b50\u00a0=permittivity of free space), then the value of n \u00a0is - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"An infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \u00a0z=\u03bbLn\u03b50\u00a0(\u00a0\u03b50\u00a0=permittivity of free space), then the value of n \u00a0is\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-infinitely-long-uniform-line-charge-distribution-of-charg\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-26T12:33:28+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"An infinitely long uniform line charge distribution of charge per unit length\u00a0\u03bb\u00a0lies parallel to the y-axis in the y-z plane at\u00a0z=32a\u00a0 (see figure). 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