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Question

# Two charged conducting spheres of radii a and b are connected to each other by a wire. The ratio of electric fields at the surfaces of two spheres is:

A
ab
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B
ba
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C
a2b2
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D
b2a2
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Solution

## The correct option is B baLet a be the radius of a sphere A, Qa be the charge on the sphere, and Ca be the capacitance of the sphere. Let b be the radius of a sphere B, Qb be the charge on the sphere, and Cb be the capacitance of the sphere. Since the two spheres are connected with a wire, their potential (V) will become equal.Let Ea be the electric field of sphere A and Eb be the electric field of sphere B. Therefore, their ratio,⟹EaEb=Qa4πϵ0a2×4πϵ0b2Qb⟹EaEb=QaQb×b2a2However, QaQb=Ca VCb VAnd, CaCb=ab∴QaQb=ab⟹EaEb=abb2a2=baTherefore, the ratio of electric fields at the surface is ba

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