Question

Consider a uniform spherical charge distribution of radius `R_(1)` centred at the orgin `O`. In this distribution a spherical cavity fo 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

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

Answer 1

Correct Answer - D
Here, total electric field `vec(E) = vec(E_(1)) + vec(E_(2))`
`= (rho)/(3 in_(0)) vec(OA) + (rho)/(3 in_(0)) + vec(AP) = (rho)/(3 in_(0)) (vec(OA) + vec(AP))`

`vec(E) = (rho)/(3 in_(0)) (vec(OP)) = (rho)/(3 in_(0)) vec(a)`
Hence `vec(E)` is uniform and botyh its magnitude and direction depend on `vec(a)`.