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Question

A sphere of radius r has electric charge uniformly distributed in its entire volume. At a distance d from the centre inside the sphere (d < r) the electric field intensity is directly proportional to

A
1d
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B
1d2
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C
d
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D
d2
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Solution

The correct option is C d
Radius of the sphere =r.
Volume of the sphere =43πr3.
Volume charge density ρ=Total chargeVolume
ρ=Q43πr3
Now consider the sphere of radius d.
Charge encloses by sphere with radius d.
q=ρ . 43πd3
=Qd3r3
Electric field intensity
E=K.qd2
=KQdr3
As total charge and radius r is constant.
E α d
884515_955972_ans_4dc967c42d884472a74cd05671a3c0aa.png

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