The concentric, thin metallic spheres of radii `r_(1)` and `r_(2) (r_(1) gt r_(2))` carry charges `q_(1)` and `q_(2)` respectively. Then the electric potential at distance `r (r_(2) lt r lt r_(1))` will be `(1)/(4pi epsilon_(0))` times

Options

A. `(q_(1) + q_(2))/(r )`
B. `(q_(1))/(r_(1)) + (q_(2))/(r )`
C. `(q_(1))/(r_(2)) + (q_(2))/(r_(2))`
D. `(q_(1))/(r_(2)) + (q_(2))/(r_(1))`

Answer

B

Explanation

The given point is inside the larger swphere. So, potential at this point is the same as no the surface of the pshere. The value is `(1)/(4pi epsilon_(0))(q_(1))/(r_(1))`.
The given point is outside the smaller sphere. So, the charge on the smaller sphere would behave as if concentrated at the centre. the potential due to
smaller sphere is `(1)/(4pi epsilon_(0))(q_(2))/(r )`.
Applying principle of superposition of potentials, the
total potential is `(1)/(4pi epsilon_(0)) [(q_(1))/(r_(1))+(q_(2))/(r )]`