First slide

Electric field

Question

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

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