Question

Two equations are given below:
A) $\oint \overline{E}.d\overline{A}=\frac{Q}{E_0}$ B) $\oint \overline{B}.d\overline{A}=0$

• A. A - Ampere's law B - Gauss law for electricity
• B. A - Gauss law for electric fields B - Gauss law for magnetic fields
• C. A - Faraday law B- Gauss law for electric fields
• D. Both (A) and (B) represent Faraday law

Answer 1

The correct option is B A - Gauss law for electric fields B - Gauss law for magnetic fields

(A) $\oint \overrightarrow{E}.\overrightarrow{dA}=\frac{Q}{{\epsilon }_0}$ , is Gauss' law for electric fields .

Gauss' law states that the total electric flux through a closed surface is equal to $1/{\epsilon }_0$ times the magnitude of the net charge enclosed by surface i.e.

$\varphi =\frac{Q}{{\epsilon }_0}$

But , the electric flux $\varphi$ linked with a surface $A$ in an electric field $\overrightarrow{E}$ is the surface integral of the electric field over that surface ,

$\varphi =\oint \overrightarrow{E}.\overrightarrow{d}A$

Hence , $\oint \overrightarrow{E}.\overrightarrow{d}A=\frac{Q}{{\epsilon }_0}$

(B) $\oint \overrightarrow{B}.\overrightarrow{d}A=0$ ,is Gauss' law for magnetic fields .

Gauss' law states that surface integral of magnetic field $\overrightarrow{B}$ over a closed surface $A$ is always zero.