Question
Tue March 20, 2012 By:

A small spherical conductor having charge q and radius r is surrounded by a hollow metallic sphere of radius 'R' and charge Q. Show that charge will always flow from inner conductor to the outer one irrespective of charge on them.

Expert Reply
Fri June 15, 2012

Consider two concentric conducting spheres A and b of radii ‘R’ and ‘r’ ,respectively.

Such that:   R>r

Let charge on A sphere be ‘Q’ and B sphere be ‘q’.

Sphere A is hollow and B is solid.

Thus, potential on the surface of sphere A and B are:

Now.

Since,

1/r>1/R

Clearly V(r)>V(R)

Hence the potential on smaller sphere will always be greater than the larger sphere and since charge is always transferred from higher to lower potential, charge will always be transferred from smaller sphere to larger sphere irrespective of charge on those two spheres.

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