There are three concentric thin spheres of radius `a,b,c (agtbgtc)`. The total surface charge densities on their surfaces are `sigma,-sigma,sigma` respectively. The magnitude of the electric field at `r` (distance from centre) such that `agtrgtb` is:

Options

A. 0
B. `(sigma)/(epsilon_(0) r^(2))(b^(2)-c^(2))r^(3)`
C. `(sigma)/(epsilon_(0)r)(a^(2)+b^(2))`
D. none of these

Answer

B

Explanation

Electric field at a distance r(a gt r gt b) will be due to charges enclosed in r only, and since, a sphere acts as a point charge for points outside its surface.
`:. E=(kQ_(0))/(r^(2))+(kQ_(0))/(r^(2))=k/(r^(2)) (sigmaxx4pic^(2)+(-sigma)4pib^(2))=(sigma)/(epsilon_(0)r^(2))(c^(2)-b^(2))`