Two concentric spheres kept in air have radii R and r. They have similar charge and equal surface charge density `sigma`. The electrical potential at their common centre is (where, `epsi_(0) =` permittivity of free space)

Options

A. `(sigma(R+r))/(epsilon_(0))`
B. `(sigma(R-r))/(epsilon_(0))`
C. `(sigma(R+r))/(2epsilon_(0))`
D. `(sigma (R+r))/(4epsilon_(0))`

Answer

A

Explanation

Potential at the centre due to sphere 1,
`V_(1)=(1)/(4pi epsilon_(0))(q)/(R)`
and due to sphere 2 is
`V_(2)=(1)/(4pi epsilon_(0))(q)/(r)`
`therefore` Electric potential at the common centre
`V=V_(1)+V_(2)=(1)/(4pi epsilon_(0))(q)/(R)+(1)/(4pi epsilon_(0))(q)/(r)`
`V=(q)/(4pi epsilon_(0))[(1)/(R)+(1)/(r)]=(q)/(4pi epsilon_(0))[(R+r)/(Rr)]`
we have `(q)/(4pi Rr)=sigma`
`rArr" Electric potential, V"=(sigma(R+r))/(epsilon_(0))`