Two non-conducting spheres of radii R 1 and R 2 and carrying uniform volume charge densities + ρ and -…

Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and -ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
  1. the electrostatic field is zero.
  2. the electrostatic potential is constant.
  3. the electrostatic field is constant in magnitude.
  4. the electrostatic field has same direction.

Solution

In triangle PC1C2,
r→2=d→+r→1


The electrostatic field at point P is,
E→=Kρ43πR13r→2R13+Kρ43πR23-r→1R23
E→=Kρ43πr→2-r→1
E→=ρ3ε0d→

Asked in: JEE Advanced 2013 (Paper 2)

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