Consider a uniform spherical distribution of radius R₁ centred at the origin O. In this distribution, a spherical cavity of radius $R_2$ , centred at P with distance OP = a = R₁ - $R_2$ (see figure) is made. If the electric field inside the cavity at position $\vec{r}$ is $\vec{E}\left(\vec{r}\right)$ , then the correct statement(s) is(are) :
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Question

Consider a uniform spherical distribution of radius R₁ centred at the origin O. In this distribution, a spherical cavity of radius R 2 R_2 R 2 , centred at P with distance OP = a = R₁ - R 2 R_2 R 2 (see figure) is made. If the electric field inside the cavity at position r ⃗ \vec{r} r is E ⃗ ( r ⃗ ) \vec{E}\left(\vec{r}\right) E ( r ) , then the correct statement(s) is(are) :

Physics · Electrostatic

JEE Advanced 2015

G1 Physics · Accepted Answer

Step 1: Use superposition, 𝐄 = Σ[1/(4πε₀)] qᵢ 𝐫ᵢ/rᵢ³, or the appropriate continuous-distribution integral. Step 2: Resolve components and exploit symmetry to cancel components. Step 3: Add the surviving components and compare with the choices. Final: D: 𝐄 is uniform and both its magnitude and direction depend on 𝐚.