Question

If the surface normal vector $\hat{n}$ makes an angle $\theta$ with the electric field $\overrightarrow{E}$, then the electric flux through a surface of area $dS$ is given by

• A. $\varphi =EdS\sin \theta$
• B. $\varphi =EdS\cos \theta$
• C. $\varphi =dS\cos \theta$
• D. $\varphi =E\cos \theta$

Answer 1

The correct option is B $\varphi =EdS\cos \theta$

We know that flux is given by $\varphi =\overrightarrow{E}.\overrightarrow{dS}$

The direction of vector $\overrightarrow{dS}$ that is area vector is along normal to surface that is $\hat{n}$.

Hence, $\varphi =EdS\cos \theta$

Answer-(B)