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Question: Answered & Verified by Expert
A charge Q is distributed over three concentric spherical shells of radii a, b, c a<b<c such that their surface charge densities are equal to one another.

The total potential at a point at distance r from their common centre, where r<a, would be:
PhysicsElectrostaticsJEE MainJEE Main 2019 (10 Jan Shift 1)
Options:
  • A Q4πϵ0a+b+c
  • B Q a2+b2+c24πϵ0a3+b3+c3
  • C Q12πϵ0ab+bc+caabc
  • D Qa+b+c4πϵ0a2+b2+c2
Solution:
2573 Upvotes Verified Answer
The correct answer is: Qa+b+c4πϵ0a2+b2+c2

Surface charge densities of all sphere is given as q1a2=q2b2=q3c2=constant, where q1q2 and q3 is charge on sphere of radius ab and c respectively.

q1+q2+q3=Q

q1=a2(Q)a2+b2+c2

q2=b2(Q)a2+b2+c2

q3=c2Qa2+b2+c2

Potential at a point where r<a is given as V=Kq1a+Kq2b+Kq3c, where K is a constant.

V=14πε0Qa+b+ca2+b2+c2

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