devarshi-dt-logo

Question:

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are E1, E2 and E3 respectively, then which of the following is correct?

E2>E1>E3

E3>E2>E1

E3>E1>E2

E1>E2>E3

Solution:

For a point outside the sphere, we have E = Q/(4πε₀R²).

  1. For sphere 1: Q → Q, R → R => E1 = Q/(4πε₀R²)
  2. For sphere 2: Q → 2Q, R → R => E2 = 2Q/(4πε₀R²) = 2E1
  3. For sphere 3: Q → 4Q, R → R => E3 = 4Q/(4πε₀(2R)²) = Q/(4πε₀R²) = E1
    Therefore, E2 > E1 = E3