Question

At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V / m$. The electric field at $3 \,cm$ from the centre of the sphere will be

• A. 150 V/m
• B. 125 V/m
• C. 120 V/m
• D. Zero

Answer 1

Answer: (C)

Electric field outside of the sphere, $E_{\text {out }}=\frac{k Q}{r^{2}} ........ (i)$
Electric field inside the dielectric sphere, $E_{ in }=\frac{k Q x}{R^{3}} ....... (ii)$
From (i) and (ii) $E_{\text {in }}=E_{\text {out }} \times \frac{r^{2} x}{R}$
$\Rightarrow $ At $3\, cm , E=100 \times \frac{3(20)^{2}}{10^{3}}=120 V / m$