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Charges Q, 2Q and 4Q are uniformly distributed inside three dielectric (non-conducting) solid spheres labelled 1, 2 and 3, having radii R/2, R and 2R respectively. The electric field magnitudes at a point P located a distance R from the centre of each sphere are E1, E2 and E3. Which ordering is correct?

1. E1 > E2 > E3
2. E3 > E1 > E2
3. E2 > E1 > E3
4. E3 > E2 > E1

Correct answer: E1 > E2 > E3

Solution

Sphere 1: radius R/2, so P at R is outside -> E1 = kQ/R². Sphere 2: radius R, P at R is on the surface -> E2 = k(2Q)/R² = 2kQ/R². Wait — recompute carefully. Sphere 3: radius 2R, P at R is inside -> E3 = k(4Q)R/(2R)³ = k*4Q*R/(8R³) = kQ/(2R²). E1 = kQ/R² = 1.0 (kQ/R² units). E2 = 2kQ/R² = 2.0. E3 = 0.5. That gives E2 > E1 > E3. The internally consistent computation gives E2 > E1 > E3.

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