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?
Solution
By Gauss law
<br><br>$$\oint {\overrightarrow E .d\overrightarrow A } = {{{q_{in}}} \over {{\varepsilon _0}}}$$
<br><br>When ${\overrightarrow E ||\overrightarrow A }$ and ${\left| {\overrightarrow E } \right|}$ is constant then
<br><br>$E\int {dA} = {{{q_{in}}} \over {{\varepsilon _0}}}$
<br><br>$\Rightarrow$EA = ${{{q_{in}}} \over {{\varepsilon _0}}}$
<br><br>$\therefore$ ${\left| {\overrightarrow E } \right|}$ should be constant on the surface and the
surface should be equipotential.
About this question
Subject: Physics · Chapter: Electrostatics · Topic: Gauss's Law
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