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 gtE_3`
B. `E_3 gt E_1 gtE_2`
C. `E_2 gt E_1 gtE_3`
D. `E_3 gt E_2 gtE_1`

Answer

C

Explanation

`E_1= (KQ)/(R^2)`
`E_2= (K2Q)/(R^2) = (2KQ)/(R^2) =2E_1`
`E_3 = (K xx4Q xxR)/((2R)^3)=(KQ)/(2R^2)=E_1/2`
`E_2 gt E_1 gt R_3`