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Question

Two charged spheres of radii R1 and R2 have equal surface charge density. The ratio of their potential at an equidistant external point is

A
R2R1
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B
(R2R1)2
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C
(R1R2)2
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D
R1R2
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Solution

The correct option is D R1R2
Given two spheres of radii R1 and R2 have equal surface charge density.
To find the ratio of their potentials at an equidistant external point.

Let us suppose that the sphere with radius R1 has charge q1 on it, and that the sphere with radius R2 has a charge q2 on it. Now, they have same charge densities, so q14πR12=q24πR22
So, q1q2=(R1R2)2 ...(i)

Potential in first sphere, V1=kq1R1
Potential in second sphere, V2=kq2R2
Thus, V1V2=q1R1.R2q2
=q1q2(R1R2)2

From (i), V1V2=(R1R2)2×R1R2=R1R2

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