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Q.

Let there be a spherically symmetric charge distribution with charge density varying as  ρ(r)=ρ054−rR  up to   r=R   and ρ(r)=0 for r>R, where r is the distance from the origin. The electric field at a distance r(r>R) from the origin is given by

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a

ρ0r4ε053−rR

b

4πρ0r3ε054−rR

c

2ρ0r4ε054−rR

d

ρ0r3ε054−rR

answer is A.

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Detailed Solution

Let us consider a spherical shell of radius x and thickness dx .Charge on this shelldq=ρ.4πx2dx=ρ054−xR⋅4πx2dx  Total charge in the spherical region from centre to r (r
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