First slide

Electric field

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

Moderate

A

150 V/m
B

125 V/m
C

120 V/m
D

Zero

Solution

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 (1) and (11), $E_{in} = E_{out} \times \frac{r^{2} x}{R}$
$\Rightarrow At 3 cm, E = 100 \times \frac{3 {(20)}^{2}}{10^{3}} = 120 V / m$

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