Consider a uniformly charged solid sphere of radius R and volume charge density ρ. A spherical cavity of radius R/2 is carved out as shown. Find the ratio of ∣ E ⃗ A ∣ ∣ E ⃗ B ∣ \frac{\left\vert\vec{E}_{A}\right\vert}{\left\vert\vec{E}_{B}\right\vert} ∣ E B ∣ ∣ E A ∣ of the magnitudes of the electric fields E ⃗ A \vec{E}_{A} E A and E ⃗ B \vec{E}_{B} E B at points A and B due to the remaining charge distribution.
Physics · Electrostatic
JEE Mains 2020

Question

Consider a uniformly charged solid sphere of radius R and volume charge density ρ. A spherical cavity of radius R/2 is carved out as shown. Find the ratio of ∣ E ⃗ A ∣ ∣ E ⃗ B ∣ \frac{\left\vert\vec{E}_{A}\right\vert}{\left\vert\vec{E}_{B}\right\vert} ∣ E B ∣ ∣ E A ∣ of the magnitudes of the electric fields E ⃗ A \vec{E}_{A} E A and E ⃗ B \vec{E}_{B} E B at points A and B due to the remaining charge distribution.

Physics · Electrostatic

JEE Mains 2020

G1 Physics · Accepted Answer

Use superposition: the remaining body equals the original uniformly charged sphere plus a sphere of charge density -ρ occupying the cavity. Evaluate the two field vectors at A and B and add them vectorially. The resulting magnitudes give Eₐ/Eᵦ = 18/34 = 9/17. Correct answer: D.