Question

TWO THIN CONCENTRIC SHELLS OF RADII r1 AND r2(r2 >r1) HAVE CHARGES q1 AND q2. WRITE THE EXPRESSION FOR THE POTENTIAL AT THE SURFACE OF INNER AND OUTER SHELLS.

Answer 1

The net potential at the centre of the concentric thin spherical shell is due to the inner sphere of radius r and outer radius r is the total scalar sum of potential due to each spheres at the centre
The first expression for the potential at the surface of the smaller sphere will be kq1/r1

Potential at any point is negative of work don
(1)r2drVr = Kq∫∞r1r2drVr = Kq-1rr∞ = -
Kq0-1r = KqrVr = Kqr

while the second expression is the potential as the surface of larger sphere will be Kq /r
As the potential is same throughout the inner portion of a hollow sphere of radius R as on its surface
and we know that the potential due to a hollow spherical shell is kq/r at any distance r from the center
when r is greater than or equal to R
while when r is less than R then the potential at any point will be kq2/R2 , where R is the radius of the hollow sphere.
as the electric field is zero inside a hollow sphere.

so,
Part 1:
Vi= kq1/r1 + kq2/r2

Part 2:
The potential at the outer shell will be
Vo= k (q1+ q2)/ r2

Assuming total charge to be at the centre of the system and thereby finding the potential at a distance R from the centre.