A long cylinder of radius R is charged with a volume charge density ρ=3r3 forr≤R =0forr>R, where r is the distance measured from the axis of the cylinder, then
A
The charge contained in L length of the cylinder for r>R is 6π5R5L
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B
The electric field at r<R is 3r45ϵ0
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C
The electric field at r>R is 3R55ϵ0r
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D
The electric field at r<R is 2r45ϵ0
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Solution
The correct options are A The charge contained in L length of the cylinder for r>R is 6π5R5L B The electric field at r<R is 3r45ϵ0 C The electric field at r>R is 3R55ϵ0r r≤Rρ=dqdv⇒dq=ρ(dv)=ρ(2πrLdr)⇒dq=(3r3)(2πrLdr)⇒q=∫R06πLr4dr=6πR55LForr<R,∫Eds=qinϵ0=6πLr55ϵ0⇒E.2πrL=6πLr55ϵ0⇒E=3r45ϵ0Forr>R,E.2πrL=6πLR55⇒E=3R55ϵ0r