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Question

A sphere of radius R carries charge density proportional to the square of the distance from the center. ρ=Ar2, where A is a positive constant. At a distance of R/2 from the center, the magnitude of the electric field is :

A
A/4πϵ0
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B
AR3/40ϵ0
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C
AR3/24ϵ0
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D
AR3/5ϵ0
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Solution

The correct option is C AR3/24ϵ0
Accordingtoquestion..............chargedensityP=chargeenclosedVolumeofsphere=QV=Q43πr3fromGaussLaw:ElectricfieldEatdistancerfromcentre=QA.E0=p.VA.E0=p.(43πr3)4πr3=pr3.E0ElectricfieldatdistanceR2fromcentre=p(R2)3.E0Also,p=Ar2so,patR2=A×R24ElectricfieldatdistanceR2fromcentre=[A.R24](R2)3.E0=A.R324.E0sothatthecorrectoptionisC.

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