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Question
Two spheres A and B of radius a and b respectively are at the same potential. Find the ratio of the surface charge densities of A and B.
Solution
Since the electric potential is the same, `1/(4piepsilon_0) "Q"_1/"a" = 1/(4piepsilon_0) "Q"_2/"b"`
∴ `"Q"_1/"Q"_2 = "a"/"b"`
But σ1 = `"Q"_1/(4pi"a"^2)` and σ2 = `"Q"_2/(4pi"b"^2)`
∴ `σ_1/σ_2 = "Q"_1/"Q"_2 xx "b"^2/"a"^2 = "a"/"b" xx "b"^2/"a"^2 = "b"/"a"`
The ratio of the surface charge densities of A and B is b : a.
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