Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii `R//2`, R and 2R respectively, as shown in figure. If magnitude of the electric fields at point P at a distance R from the centre of sphere 1,2 and 3 are `E_1, E_2 and E_3` respectively, then

Options

A. `E_(1) gt E_(2) gt E_(3)`
B. `E_(3) gt E_(1) gt E_(2)`
C. `E_(2) gt E_(1) gt E_(3)`
D. `E_(3) gt E_(2) gt E_(1)`

Answer

C

Explanation

`E_(1) = (kQ)/(R^(2)) , ` where `k = (1)/(4 pi epsi_(0))`
`E_(2) = (k(2Q))/(R^(2)) rArr E_(2) = (2KQ)/(R^(2)) , E_(3) = (K (4Q)R)/((2R)^(3)) rArr E_(3) = (Kq)/(2R^(2)) therefore E_(2) gt E_(1) gt E_(3)`