Two infinite identical charged sheets and a charged spherical body of charge density ' ρ ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is:

Solution

Physics sir · 5 steps

The sheets cancel between them, so the sphere alone sets A and B; outside, check direction too.

1. Field of the sheets. Each sheet gives σ/2ε₀, pointing away from it on both sides. Between the two identical sheets the two fields point opposite ways and cancel. Outside they point the same way and add to σ/ε₀.
2. Field of the sphere. Outside the sphere, Gauss's law gives the field of a point charge at the centre. It weakens as 1/r², where r is the distance from the centre.

   Eₛₚₕₑᵣₑ = (ρ R³)/(3ε₀ r²)

3. Points A and B. Both lie between the sheets, so only the sphere's field acts there. A is closer to the sphere than B, so E_A > E_B.
4. Points C and D. At C the field points left, and at D it points right, so the two vectors cannot be equal. Their sizes differ too: both get σ/ε₀ from the sheets, but D is much closer to the sphere than C is.
5. So. E⃗_A > E⃗_B and E⃗_C ≠ E⃗_D, which is option (c).

The idea to keep. Two identical sheets give zero field between them and σ/ε₀ outside. Find the sheet field first, then add the other charges point by point.

Answer from the NTA final answer key. Solution by PrepWiser.