Question

Gaussian surface measures the electric field

• A. parallel to the surface area
• B. tangent to the surface area
• C. perpendicular to the surface area
• D. anti-parallel to the surface area

Answer 1

The correct option is C perpendicular to the surface area

According to Gauss Law,

$\int \overrightarrow{E}.\overrightarrow{dS}=\frac{q_{enclosed}}{{\epsilon }_0}$

$\overrightarrow{E}.\overrightarrow{dS}$ can be written as $EdS\cos \theta$, where $\theta$ is angle made by $\overrightarrow{E}$ with area vector $\overrightarrow{dS}$ of surface element.

If $\overrightarrow{E}$ is parallel or antiparallel to surface, then $\overrightarrow{E}.\overrightarrow{dS}=EdS\cos {90}^{\circ }=0$

We cannot measure the electric field using Gauss Law.

But if $\overrightarrow{E}$ is perpendicular to the surface, then $\theta =0^{\circ }$ then $\overrightarrow{E}.\overrightarrow{dS}=EdS\cos 0^{\circ }=EdS$

So, gaussian surface measures the electric field perpendicular to surface area.