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Q.

A long solid non-conducting cylinder of radius R is charged such that the volume charge density is proportional to r where r is the distance from axis. The electric field E at a distance r (r < R) will depend on r as

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a

E∝r2

b

E∝r

c

E∝1/r2

d

E∝1/r

answer is B.

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Detailed Solution

Question Image

ρ∝r ; ρ=kr dQ=ρV=Kr2πrdr×l

Using Gauss's Law, by considering the gaussian surface as a cylinder with a radius of ‘r’

E.2πrl=∫0rKr.2πrl.drε0⇒E=Kr23ε0 ∴  E∝r2

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