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

Answer

C

Explanation

`E_(1) = (1)/(4pi in_(0)) (Q)/(R^(2)) , E_(2) = (1)/(4pi in_(0)) (2Q)/(R^(2))` ,
`E_(3) = (1)/(4pi in_(0)) ((4Q) R)/(8 R^(3)) = (1)/(4pi in_(0)) (Q)/(2 R^(2))`
Thus `E_(2) gt E_(1) gt E_(3)`