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

Answer

A

Explanation

The potential outside the surface, on the surface and at any point inside the surface is same, `therefore" "V_(1)=1/(4piepsi_(0))q/R`
`" "(thereforesigma=q/(4piR^(2))thereforeq=sigma4piR^(2))`
`therefore" "V_(1)=1/(4piepsi_(0))(sigma4piR^(2))/R`
`V_(1)=(sigmaR)/epsi_(0)`
Similarly,`" "V_(2)=(sigmar)/epsi_(0)`
Thus, the resultant potential is given by,
`V=V_(1)+V_(2)`
`=(sigmaR)/epsi_(0)+(sigmar)/epsi_(0)=sigma/epsi_(0)(R+r)`