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A metal sphere A of radius a is charged ...

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

A

`b/a V`

B

`a/b V`

C

`a^2/b V`

D

`a/b^2 V`

Text Solution

Verified by Experts

The correct Answer is:
B
If q is charge on sphere A, Fig. then potential of A is.

`V = (q)/(4pi in_(0) a) :. Q = (4pi in_(0) a)V` …(i)
When A is enclosed by a spherical conducting shell B, and the two are connected by a wire, the entire charge q of A shifts to outer surface of B.
`:.` Potenitial of B will be
`V_(B) = (q)/(4pi in_(0) b) = (4pi in_(0) a)/(4pi in_(0) b)` , using (i)
`V_(B) = (a)/(b) V`
As sphere, A is inside B, therefore, final potential
of `A = V_(A) = V_(B) = (a)/(b) (V) , i.e, V_(A) lt V`.
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