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Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region: $Image$
$(A)$ 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
$(C,D)$
$(B,D)$
$(B,C)$
$(A,C)$
Solution
For electrostatic field,
$\vec{E}_P=\vec{E}_1+\vec{E}_2 $
$=\frac{\rho}{3 \varepsilon_0} \overrightarrow{ C _1 P }+\frac{(-\rho)}{3 \varepsilon_0} \overrightarrow{ C _2 P } $
$=\frac{\rho}{3 \varepsilon_0}\left(\overrightarrow{ C _1 P }+\overrightarrow{ PC _2}\right)$
$\overrightarrow{ E }_{ p }=\frac{\rho}{3 \varepsilon_0} \overrightarrow{ C _1 C _2}$
For electrostatic potential, Since electric field is non zero so it is not equipotential.
