Q. 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
Explanation
(c) Electric field outside of the sphere $E_{out} = \frac{kQ}{r^{2}}$ …(i)
Electric field inside the dielectric sphere $E_{in} = \frac{kQx}{R^{3}}$ …(ii)
From (i) and (ii), $E_{in} = E_{out} \times \frac{r^{2}x}{R^{3}}$
$\Rightarrow At\ 3\ cm,\ E = 100 \times \frac{3(20)^{2}}{10^{3}} = 120V/m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.