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Question

# A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the center. What is the ratio of the magnitude of the electric field at distance 2R from the center to the magnitude of the electric field at a distance of R/2 from the center?

A
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B
2
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C
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D
8
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Solution

## The correct option is D 2Given that volume charge density ρ=Cr2Total charge on the sphere q=∫r04πr2drρ=∫r04πCr4dr=45πCr5Er=R/2kq(r=R/2)(R/2)2=k(4/5)πC(R/2)5(R/2)2Er=2R=kq(r=R)(2R)2=k(4/5)πCR54R2Now solve to get Er=2REr=R/2=2

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