Two conducting spheres of radii r1 and r2 are equally charged.The ratio of their potential is?

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Solution

Both the spheres have the same surface charge densities.

Let us suppose that the sphere with radius R1 has a charge q1 on it, and that the sphere with radius R2 has a charge q2 on it.

Now,

q1/[4π(R1)²] = q2/[4π(R2)²]

=> q1/R1² = q2/R2² => q1/q2 = (R1/R2)²

Potential in first sphere = V1 = kq1/R1

Potential on second sphere = V2 = kq2/R2

Thus, V1/V2 = q1.R2/q2.R1

= (q1/q2).(R2/R1)

=(R2/R1).

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