A metal sphere A of radius a is charged to potential V. What will be its potential if it is enclosed ny a spherical conducting shell B of radius b and the two are connected by a wire ?

Explanation

If the charge on the sphere of radius a is q, then
`V = (1)/(4 pi epsilon _0) q/a`
`i.e, q = (4 pi epsilon_0 a) V`
Now, when sphere A is enclosed by spherical conductor B and the two are connected by a wire, charge will reside on the outer surface of B and so the potential of B will be
`V_B= (1)/(4 pi epsilon _0) q/b = (1)/(4 pi epsilon_0)(4pi epsilon_(0)a)/(b)V = a/b V`
Now as sphere A is inside B, so its potential is
`V_A = V_B = a/b (V)" " [ V "as a" lt b]`.
(##BMS_V03_C03_S01_031_S01##).