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JEE Main201910 Jan 2019Morning ShiftPhysicsElectrostaticsActual

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:

Options

  1. AQ 4 π ϵ 0 a + b + c
  2. BQ a 2 + b 2 + c 2 4 π ϵ 0 a 3 + b 3 + c 3
  3. CQ 12 π ϵ 0 a b + b c + c a a b c
  4. DQ a + b + c 4 π ϵ 0 a 2 + b 2 + c 2

Correct answer

D. Q a + b + c 4 π ϵ 0 a 2 + b 2 + c 2

Step-by-step solution

Surface charge densities of all sphere is given as q 1 a 2 = q 2 b 2 = q 3 c 2 = c o n s t a n t , where q 1 , q 2 and q 3 is charge on sphere of radius a , b and c respectively. q 1 + q 2 + q 3 = Q q 1 = a 2 ( Q ) a 2 + b 2 + c 2 q 2 = b 2 ( Q ) a 2 + b 2 + c 2 q 3 = c 2 Q a 2 + b 2 + c 2 Potential at a point where r < a is given as V = K q 1 a + K q 2 b + K q 3 c , where K is a constant. V = 1 4 π ε 0 Q a + b + c a 2 + b 2 + c 2

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