Two non-conducting spheres of radii $R_{1}$ and $R_{2}$ 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,

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the electrostatic field is zero

the electrostatic potential is constant

the electrostatic field is constant in magnitude

the electrostatic field has same direction

answer is C, D.

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Detailed Solution

In an electrostatic field,

$E_{p} = E_{1} + E_{2} = \frac{ρ}{3 ε_{0}} C_{1} P + \frac{(- ρ)}{3 ε_{0}} C_{2} P E_{p} = \frac{ρ}{3 ε_{0}} (C_{1} P + C_{2} P) E_{p} = = \frac{ρ}{3 ε_{0}} C_{1} C_{2}$

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