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Question

Let ρ(r)=Qr4πR4 be the charge density distribution of a solid sphere of radius R and total charge Q. Find the magnitude of electric field at a point P inside the sphere at a distance r1 from the centre of the sphere.

A
Q4π2ϵ0r12
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B
Qr124π2ϵ0R4
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C
Qr1216πϵ0R4
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D
0
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Solution

The correct option is C Qr1216πϵ0R4


Given that,

The charge density ρ(r)=Qr4πR4

According to the fig,

The electric field at the point P distant r1 from the center,

According to gauss’s theorem

E×4πr21= charge enclosed/ε0

E×4πr21=1ε0ρdV

E×4πr21=1ε0r10Qr4πR4×4πr2dr

E=1ε0×Qr414×4πR4×4π×14πr21

E=Qr21ε016πR4

Therefore, the electric field at a point P will be; E=Qr21ε016πR4


981734_591939_ans_c853c5a0f8374050b248fe910830ea53.png

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