Question

Electric field in a space varies $\overrightarrow{E}=(x\hat{i}+10\hat{j})$ where $x$ is in meter. Then the total charge contained within a prism as shown is

• A. ${ϵ}_0$
• B. $2{ϵ}_0$
• C. $5{ϵ}_0$
• D. $6{ϵ}_0$

Answer 1

The correct option is D $6{ϵ}_0$

Varies, $\overline{E}=(r\hat{i}+10\hat{j})$ or $E=\frac{q\times d}{{ϵ}_0}$

total charge $={ϵ}_{0}E=q\times d$

$E=\frac{1}{4\pi {ϵ}_0}\frac{q}{d^2}$ or $q=\frac{E{ϵ}_0}{d}$

$=9\times {10}^9\times 9$ or $=\frac{12{ϵ}_0}{2}$

$=9+100$ $=6{ϵ}_0$