Question 557: Electrostats & Capacitance

Question

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?

Accepted Answer

By Gauss law
$$\oint {\overrightarrow E .d\overrightarrow A }  = {{{q_{in}}} \over {{\varepsilon _0}}}$$
When $${\overrightarrow E ||\overrightarrow A }$$ and $${\left| {\overrightarrow E } ight|}$$ is constant then
$$E\int {dA}  = {{{q_{in}}} \over {{\varepsilon _0}}}$$
$$ \Rightarrow $$EA = $${{{q_{in}}} \over {{\varepsilon _0}}}$$
$$ 	herefore $$ $${\left| {\overrightarrow E } ight|}$$ should be constant on the surface and the
surface should be equipotential.

Answer

Only when $$\left| {\overrightarrow E } \right|$$ = constant on the surface.

Answer

For any choice of Gaussian surface.

Answer

Only when the Gaussian surface is an
equipotential surface.

Answer

Only when the Gaussian surface is an
equipotential surface and $$\left| {\overrightarrow E } \right|$$ is constant on
the surface.

Electrostats & Capacitance

Choose the correct answer: