{"id":5164,"date":"2022-04-06T17:47:07","date_gmt":"2022-04-06T17:47:07","guid":{"rendered":"https:\/\/physics.educour.in\/isc-physics\/?p=5164"},"modified":"2022-04-07T07:33:33","modified_gmt":"2022-04-07T07:33:33","slug":"application-of-gauss-law","status":"publish","type":"post","link":"https:\/\/physics.educour.in\/isc-physics\/application-of-gauss-law\/","title":{"rendered":"Application of Gauss’ Law"},"content":{"rendered":"\t\t
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(Short Notes)<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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1. Electric field due to line charge (infinite length)<\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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The electric field at a distance r from a line charge (of Charge density \u03bb) is<\/p>

\"\".
The direction is outward perpendicular to the line charge. The E \u221d (1\/r) dependence is shown in fig.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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2. Electric field due to a Uniformly Charged Cylinder<\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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If the line charge is a cylinder of radius R and carrying charge per unit length \u03bb, then<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(a) Electric field outside<\/h5>
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"<\/div>
(b) Electric field on the surface<\/h5>
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"<\/div>
\u00a0<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(c) Electric field inside (at a distance r from the axis)<\/h5>
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \"\"<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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The direction of the field is outwards (normal to the axis)
The dependence of the field is shown in figure.2 (b) Inside the charged cylinder, E \u221d r and outside the cylinder\u00a0 \u00a0 E \u221d 1\/r\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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3. Electric field due to a plane sheet (infinite dimensions)<\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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(a) Single sheet of charge<\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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For the surface charge density \u03c3 (coulomb\/metre2<\/sup>) the field at a distance r from the sheet is\u00a0\"\"directed towards outward normal (from <\/span>a positively charged sheet)The electric field does not depend on distance.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(b) Charged metal plate<\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Inside charged metal plate E = 0<\/strong>
Outside charged metal plate \"\"<\/p>

The field is normally outwards for positively charged plate and inwards
for negatively charged plates.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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4. Electric field due to a charged spherical shell or charged conducting sphere<\/h4>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The charge Q resides on the surface of the spherical shell (radius R).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(a) Field at outside point A<\/h5>
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \"\"<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(b) Field at surface point B<\/h5>
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \"\"<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(c) Field at inside point C<\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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E = 0 (at every point)<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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The variation of field with distance r from the centre O of the shell in shown in fig. The field at the surface is maximum. And outside the shell field varies as E \u221d 1\/r2<\/sup> .<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Special note : <\/strong><\/span>The surface charge density in the above case is \u03c3 = Q\/4\u03c0R2<\/sup>. In terms of \u03c3:\u00a0<\/p>

(a) Field outside\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><\/strong>\"\"<\/p>


<\/b><\/span>(b) Field on surface\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><\/strong>\"\"<\/p>


<\/b><\/span>(c)Field inside\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0E = 0<\/span><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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5. Electric field due to a charged sphere\u00a0<\/h4>

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\u00a0In case of a charged non conducting (plastic etc.) sphere, charges do not flow. As a result, charges exist inside the sphere as well as on the surface. Assuming uniform charge distribution, the electric field, outside (point A), on the surface (point B) and inside (point C) are as follows.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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(a) Field outside the sphere<\/span><\/strong>
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"<\/p>

Directed radially outwards (for positive Q)
(b) Field on the surface\u00a0 \u00a0 \u00a0 \u00a0<\/span><\/strong>\"\"<\/p>

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Directed radially outwards (for positive Q)<\/span><\/p>

(c) Field inside the Sphere<\/span><\/strong><\/p>

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\"\"<\/p>

\u00a0<\/p>

\u00a0<\/p>

\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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directed radially outwards for positive Q. For negetive charge it is directed inward.
The variation of the electric field with distance r from the centre of the charged nonconducting sphere is as shown in fig. The field outside varies inversely as square of the distance. The field at the surface is maximum.
The field inside the sphere is directly proportional to the distance.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Special note :<\/span><\/strong> The volume charge density in above case, is\u00a0\"\". In terms of \u03c1, the field are<\/span><\/p>

(a) Outside Sphere:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/strong>\"\"<\/p>

(b) On surface of Sphere:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/strong>\"\"<\/p>

(c) Inside Sphere:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/strong>\"\"<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

(Short Notes) 1. Electric field due to line charge (infinite length) The electric field at a distance r from a line charge (of Charge density \u03bb) is . The direction is outward perpendicular to the line charge. The E \u221d (1\/r) dependence is shown in fig. 2. Electric field due to a Uniformly Charged Cylinder … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"post_folder":[40],"class_list":["post-5164","post","type-post","status-publish","format-standard","hentry","category-12-lecture-notes"],"_links":{"self":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts\/5164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/comments?post=5164"}],"version-history":[{"count":11,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts\/5164\/revisions"}],"predecessor-version":[{"id":5232,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/posts\/5164\/revisions\/5232"}],"wp:attachment":[{"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/media?parent=5164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/categories?post=5164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/tags?post=5164"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/physics.educour.in\/isc-physics\/wp-json\/wp\/v2\/post_folder?post=5164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}