A charge Q is distributed over two concentric conducting thin spherical shells of radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

Option 1 -

1 / 4πε₀) * [(R+r) / (R²+r²)] * Q

Option 2 -

(1 / 4πε₀) * [(R+2r) / 2(R²+r²)] * Q

Option 3 -

(1 / 4πε₀) * [(R+r) / 2(R²+r²)] * Q

Option 4 -

(1 / 4πε₀) * [(2R+r) / (R²+r²)] * Q

3 Views | Posted a month ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

σ4πr² + σ4πR² = Q ⇒ σ = Q/ (4π (R²+r²)
V_c = kq? /r + kq? /R = k (σ4πr²)/r + k (σ4πR²)/R = kσ4π (r+R)
= K (Q/ (R²+r²) (R+r)

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