Question

At a point $20cm$ from the centre of a uniformly charged dielectric sphere of radius $10cm$, the electric field is $100V/m$. The electric field at $3cm$ 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, $E_{\text{out }}=\frac{kQ}{r^2}........(i)$
Electric field inside the dielectric sphere, $E_{in}=\frac{kQx}{R^3}.......(ii)$
From (i) and (ii) $E_{\text{in }}=E_{\text{out }}\times \frac{r^{2}x}{R}$
$\Rightarrow$ At $3cm,E=100\times \frac{3(20{)}^2}{10^3}=120V/m$