Consider a uniform spherical charge distribution of radius `R_(1)` centred at the origin `O`. In this distribution a spherical cavity of radius `R_(2)`, centred at `P` with distance `OP = a = R_(1) - R_(2)` (fig) is made.If the electric field inside the cavity at position `vec(r )`, then the correct statement is

Options

A. `vec(E)` is uniform, its magnitude is independent of `R_(2)` but its direction depends on `vec(r)`.
B. `vec(E)` is uniform, its magnitude depends on `vec(R_(2))` and its direction depends on `vec(r)`
C. `vec(E)` is uniform , its magnitude is independent of a but its direction depends on `vec(a)`
D. `vec(E)` is uniform and both its magnitude and direction depend on `vec(a)`.

Answer

D

Explanation

Since the sphere carries a uniform volume charge density it will be a non-conducting sphere. Hence, no concept of conducting sphere/cavity should be used.
For a spherical cavity, in a uniformly charged sphere, we use the standard result that : `vecE=(rho veca)/(3 epsi_(0))`
Where `veca` =position vector of center of cavity WRT center of sphere.