Two non-conducting spheres of radii R_1 and R | vedclass

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Question

(A) For a point $P$ in the overlapping region,the electric field due to the first sphere is $\vec{E}_1 = \frac{\rho \vec{r}_1}{3 \varepsilon_0}$,where

Vedclass · Accepted Answer

$(C, D)$

Vedclass · Answer

(A) For a point $P$ in the overlapping region,the electric field due to the first sphere is $\vec{E}_1 = \frac{\rho \vec{r}_1}{3 \varepsilon_0}$,where $\vec{r}_1$ is the position vector of point $P$ relative to the center $C_1$.The electric field due to the second sphere is $\vec{E}_2 = \frac{-\rho \vec{r}_2}{3 \varepsilon_0}$,where $\vec{r}_2$ is the position vector of point $P$ relative to the center $C_2$.The net electric field at point $P$ is $\vec{E}_P = \vec{E}_1 + \vec{E}_2 = \frac{\rho}{3 \varepsilon_0} (\vec{r}_1 - \vec{r}_2)$.Since $\vec{r}_1 - \vec{r}_2 = \vec{C}_2 C_1$ (a constant vector),the net electric field $\vec{E}_P = \frac{\rho}{3 \varepsilon_0} \vec{C}_2 C_1$ is constant in both magnitude and direction.Since the electric field is non-zero and uniform,the potential is not constant in the overlapping region.Therefore,statements $(C)$ and $(D)$ are correct.

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