Question

How can we change flux through a given area?

Answer 1

Step 1: Definition of Flux

1. Consider a surface element $d\overrightarrow{S}=\hat{n}dS$ in an electric field $\overrightarrow{E}$, where $\hat{n}$ is the outward unit vector normal to the surface element.
2. The quantity $d\varphi =\overrightarrow{E}.d\overrightarrow{S}$ becomes equal to the number of lines of force passing through the area $d\overrightarrow{S}$.
3. The flux of $\overrightarrow{E}$ over any arbitrary surface $S$ is given by the integral,

${\varphi }_E=\int d\varphi ={\int }_S\overrightarrow{E}.d\overrightarrow{S}$

Step 2: Magnetic Flux

For magnetic flux, if $S$ is an open surface bounded by the curve $C$ placed in a magnetic field $\overrightarrow{B}$ then the magnetic flux through the surface is,

${\varphi }_B={\oint }_S\overrightarrow{B}.d\overrightarrow{S}$

Step 2: Flux versus Area

1. Therefore from the above formula, we can see that flux varies with the area $d\overrightarrow{S}$.
2. Hence, for a constant electric field, the flux passing through the surface element is directly proportional to the area $d\overrightarrow{S}$.
3. In order to change flux by keeping the area constant either $\overrightarrow{B}$, $\overrightarrow{E}$ or $\theta$ must be changed.

Hence, flux changes proportionally with the area.