Question

Two charged conducting spheres of equal surface charge densities have radii R1 and R2 If the potential at the centre is V1 and V2 respectively, then

Answer 1

Heya mate..

Given Two charged conducting spheres of radii r1 and r2 have equal surface charge density.What is the ratio of their potential at center?

Given the spheres have same surface charge densities. Let sphere with radius r1 has a charge q1 on it and sphere with radius r2 has charge q2 on it.

Now q1 / 4 πr1^2 = q2 / 4 π r2^2

 So q1 / r1^2 = q2 / r2^2

  q 1 / q2 = (r1 / r2)^2

 Now potential in first sphere will be V1 = kq1 / r1

 Potential on second sphere = V2 = kq2 / r2

So V1 / V2 = q1 r2 / q2r1

q 1 / q2 x r2/r1  

= r1 / r2