We have two metal spheres of radii r1 and r2 are charged to the same potential.the ratio o charge on the spheres is
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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)=(R1/R2).
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)=(R1/R2).
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