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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?
  1. 4
  2. 8
  3. 1
  4. 2

A
2
B
8
C
4
D
1
Solution
Verified by Toppr

Given that volume charge density ρ=Cr2
Total charge on the sphere q=r04πr2drρ=r04πCr4dr
=45πCr5
Er=R/2kq(r=R/2)(R/2)2=k(4/5)πC(R/2)5(R/2)2
Er=2R=kq(r=R)(2R)2=k(4/5)πCR54R2
Now solve to get Er=2REr=R/2=2

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