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Question

# A hollow dielectric sphere has R1 and R2 as its inner and outer radii. The total charge carried by the sphere is +Q which is uniformly distributed throughout the dielectric sphere between R1 and R2. The electric field for R1<r<R2 is given by :

A
Q4πrR1
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B
Q4πr2
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C
Q4πR21
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D
Q(r3R21)4πr2(R32R31)
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Solution

## The correct option is D Q(r3−R21)4π∈r2(R32−R31) If ρ be the volume charge density, charge Q=ρ.43π(R32−R31)....(1) Let E be the electric field at r. Using Gauss's law, E.4πr2=Qenϵ where ϵ is the permittivity of dielectric medium. or E.4πr2=ρ.43π(r3−R31)ϵ or E=Q(r3−R31)4πϵr2(R32−R31) using (1)

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