JEE MAIN - Physics (2020 - 8th January Morning Slot - No. 8)
In finding the electric field using Gauss Law
the formula $$\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}}$$ is applicable. In the
formula $${{\varepsilon _0}}$$ is permittivity of free space, A is the
area of Gaussian surface and qenc is charge
enclosed by the Gaussian surface. The equation
can be used in which of the following situation?
Only when $$\left| {\overrightarrow E } \right|$$ = constant on the surface.
For any choice of Gaussian surface.
Only when the Gaussian surface is an
equipotential surface.
Only when the Gaussian surface is an
equipotential surface and $$\left| {\overrightarrow E } \right|$$ is constant on
the surface.
Explanation
By Gauss law
$$\oint {\overrightarrow E .d\overrightarrow A } = {{{q_{in}}} \over {{\varepsilon _0}}}$$
When $${\overrightarrow E ||\overrightarrow A }$$ and $${\left| {\overrightarrow E } \right|}$$ is constant then
$$E\int {dA} = {{{q_{in}}} \over {{\varepsilon _0}}}$$
$$ \Rightarrow $$EA = $${{{q_{in}}} \over {{\varepsilon _0}}}$$
$$ \therefore $$ $${\left| {\overrightarrow E } \right|}$$ should be constant on the surface and the surface should be equipotential.
$$\oint {\overrightarrow E .d\overrightarrow A } = {{{q_{in}}} \over {{\varepsilon _0}}}$$
When $${\overrightarrow E ||\overrightarrow A }$$ and $${\left| {\overrightarrow E } \right|}$$ is constant then
$$E\int {dA} = {{{q_{in}}} \over {{\varepsilon _0}}}$$
$$ \Rightarrow $$EA = $${{{q_{in}}} \over {{\varepsilon _0}}}$$
$$ \therefore $$ $${\left| {\overrightarrow E } \right|}$$ should be constant on the surface and the surface should be equipotential.
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