A sphere of radius `R` has a uniform distribution of electric charge in its volume. At a distance `x` from its centre, for `x lt R`, the electric field is directly proportional to

Options

A. `E prop r^(-2)`
B. `E prop r^(-1)`
C. `E prop r`
D. `E prop r^(2)`

Answer

C

Explanation

Electric field due to a uniform charged sphere of charge density `rho` and radius R at a distance r from the centre is given by
(i) `E = (rho r)/(3 epsilon_(0)) = (Qr)/(4pi epsilon_(0)R^(3))` (For `r lt R)`
where `rho = (Q)/((4)/(3)pi R^(3))`
(ii) `E = (1)/(4pi epsilon_(0)) (Q)/(r^(2))` (For `r gt R`)
(iii) `E = (1)/(4pi epsilon_(0)) (Q)/(R^(2))` (For r = R)