Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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A Charge Q is Placed at the Centre of an Imaginary Hemispherical Surface. Using Symmetry Arguments and Gauss'S Law - Physics

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ConceptElectric Field Introduction of Electric Field

Question

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and Gauss's Law, find the flux of the electric field due to this charge through the surface of the hemisphere in the following figure.

Solution

From Guass's law, flux through a closed surface, `phi = "Q"_("e""n")/∈_0,`

where
Qen = charge enclosed by the closed surface
Let us assume that a spherical closed surface in which the charge is enclosed is Q.
The flux through the sphere,

`phi = "Q"/∈_0`

Hence for a hemisphere(open bowl), total flux through its curved surface,

`phi′ = "Q"/∈_0 xx 1/2 = "Q"/(2∈_0)`

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Solution A Charge Q is Placed at the Centre of an Imaginary Hemispherical Surface. Using Symmetry Arguments and Gauss'S Law Concept: Electric Field - Introduction of Electric Field.
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