Question

There is an electric field $\overrightarrow{E}=\frac{a{x}^3\hat{i}+b{y}^4\hat{j}+c{z}^2\hat{k}}{a{x}^4+b{y}^5+c{z}^3}$ at any (x,y,z) coordinates in the space except origin, Where a,b & c are constant. Find the electrostatic flux passing through a sphere of radius R whose center is at the origin.

• A. $\pi R$
• B. $2\pi R$
• C. $4\pi R$
• D. Zero

Answer 1

The correct option is A $\pi R$

Flux$=\int E.ds$

Where $ds=$ area with unit vector $\to \frac{xi+yj+zk}{\sqrt{x^2+y^2+z^2}}$

Flux$=\frac{a{x}^3\hat{i}+b{y}^4\hat{j}+c{z}^2\hat{k}}{a{x}^4+b{y}^4+c{z}^3}\times \frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}}=\left(\frac{ads}{4R}\right)=\left(\frac{a}{4R}\right)\times \frac{4\pi R^2}{a}=\pi R$