Question

Consider a uniform spherical charge distribution of radius R₁ centred at the origin O. In this distribution, a spherical cavity of radius R₂, centred at P with distance OP = a = R₁ - R₂ (see figure) is made. If the electric field inside the cavity at position \(\vec{r}\) is \(\vec{E}(\vec{r})\), then the correct statement(s) is(are)

(A) \(\vec{E}\) is uniform, its magnitude is independent of R₂ but its direction depends on \(\vec{r}\)

(B) \(\vec{E}\) is uniform, its magnitude depends on R₂ and its direction depends on \(\vec{r}\)

(C) \(\vec{E}\) is uniform, its magnitude is independent of α but its direction depends on \(\vec{a}\)

(D) \(\vec{E}\) is uniform and both its magnitude and direction depend on a

Answer 1

(D) \(\vec{E}\) is uniform and both its magnitude and direction depend on a

C₁ ⇒ center of sphere and C₂ ⇒ center of cavity.