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

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 :

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E ∝ r-2

E ∝ r-1

E ∝ r0

E ∝ r

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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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