Question

A hemispherical surface of radius R is centred at the origin with its apex P on the x axis. The electric field in the region is \(\vec {E}=E_0x~\hat {i}\)
The flux of electric field through the hemishperical surface is

• A. $\pi E_0{R}^3$
• B. $\frac{4\pi }{3}{E}_0{R}^3$
• C. $\frac{2\pi }{3}{E}_0{R}^3$
• D. $2E_0{R}^3$

Answer 1

The correct option is C $\frac{2\pi }{3}{E}_0{R}^3$



$\varphi ={\int }_0^{\frac{\pi }{2}}Rd\theta .2\pi R\sin \theta E_{0}R{\cos }^2\theta$

${\begin{array}{c}=2\pi E_0{R}^3(-\frac{{\cos }^3\theta }{3})\end{array}|}_0^{\pi /2}=\frac{2\pi }{3}{E}_0{R}^3$