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

Answer

b

Explanation

Electric field at a distance`r(agtrgtb)` 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_(c ))/(r^(2))+(kQ_(b))/(r^(2))=(k)/(r^(2))(sigmaxx4pic^(2)+(-sigma)4pib^(2))`
`=(sigma)/(epsilon_(0)r^(2))(c^(2)-b^(2))`