Two metal spheres `("radii" r_1, r_2 "with" r_1 lt r_2)` are very far apart but are connected by a thin wire. If their combined charges is Q, then what is their common potential ?

Options

A. `k Q//(r_1 + r_2)`
B. `kQ//(r_1 - r_2)`
C. `-k Q//(r_1 + r_2)`
D. `-kQ//r_1 r_2`

Answer

a

Explanation

`V_C = V_1 = V_2`
`(kq_1)/r_(1) = (kq_2)/r_(1)`
`q_(1)/q_(2) = r_(1)/r_(1)` …(i)
`q_1 + q_2 = Q` …(ii)
From Eqs. (i) and (ii), we get
`q_1 = (Q r)/(r_1 + r_2)`
Putting `V_(1)`, we get
`V_(C )=(kQ)/(r_(1)-r_(2))`