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Consider metallic spheres of different radii r, all at the same electr

June 1, 2025 by rawan239

Consider metallic spheres of different radii r, all at the same electrostatic potential. Then the magnitude E of the electric field just outside these spheres depends on r as :

E ∝ r<sup>-2</sup>

E ∝ r<sup>-1</sup>

E ∝ r<sup>0</sup>

E ∝ r

This question was previously asked in

UPSC Geoscientist – 2024

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For a metallic sphere (conductor), the charge resides on its surface. The electrostatic potential V at the surface of a conducting sphere of radius r with charge Q is given by V = Q / (4πε₀r). The electric field E just outside the surface is given by E = Q / (4πε₀r²).

Given that all spheres are at the same electrostatic potential V, we can express the charge Q in terms of V and r: Q = V * (4πε₀r). Substitute this expression for Q into the formula for E.

E = Q / (4πε₀r²) = [V * (4πε₀r)] / (4πε₀r²) = V / r. Since V and 4πε₀ are constants for all spheres, the magnitude of the electric field just outside the sphere depends on the radius as E ∝ 1/r, which is E ∝ r⁻¹.

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