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

Question

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 (A) the electrostatic field is zero (B) the electrostatic potential is constant (C) the electrostatic field is constant in magnitude (D) the electrostatic field has same direction

Tardigrade Admin · Accepted Answer

For electrostatic field. Ep=E1+E2= (ρ/3 ε0)C1P+ ((-ρ)/3 ε0)C1P = (ρ/3 ε0)(C1P+PC2) Ep= (ρ/3 ε0)C1C2

Q. Two non-conducting spheres of radii $R_{1} an d R_{2}$ 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

the electrostatic field is zero

the electrostatic potential is constant

the electrostatic field is constant in magnitude

the electrostatic field has same direction

For electrostatic field.
$E_{p} = E_{1} + E_{2} = \frac{ρ}{3 ε _{0}} C_{1} P + \frac{( - ρ )}{3 ε _{0}} C_{1} P$
$= \frac{ρ}{3 ε _{0}} (C_{1} P + P C_{2})$
$E_{p} = \frac{ρ}{3 ε _{0}} C_{1} C_{2}$

Q. Two non-conducting spheres of radii R1​andR2​ 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