Question

A charge q is distributed over two concentric hollow spheres of radius smaller and capital are such that the surface charge densities are equal find the potential at the common centre

Answer 1

if we want the potential of a sphere, we need the radius (given) and the charge on it (which is what we should find now).

If the total charge is Q, then let’s assume charge of small sphere si q1, and large sphere is q2.

Thus Q = q1 + q2

It is given that the surface charge density is the same, thus:

(q1)/(4*pi*r^2) = (q2)/(4*pi*R^2).

Therefore,

q1 = (r^2)(q2)/(R^2)

But q1 + q2 = Q,

therefore,

q2 = Q(R^2)/(r^2 + R^2),

and similarly (from the same equation,

q1 = Q(r^2)/(r^2 + R^2).

Potential at common centre is now given as:

k(q1)/r + k(q2)/R.

Substituting previously found values, this becomes:

k(Q)(r+R)/(r^2 + R^2).

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Answer 2

I hope you will understand...