Question

Two concentric conducting spheres of radii $r_{1}$ and $\left(\text{r}\right)_{\text{2}}\left(\left(\text{r}\right)_{\text{1}} \left(\text{ < r}\right)_{\text{2}}\right)$ carry electric charges of $+ \, Q$ and $-Q$ respectively. The region between the sphere is filled with two insulating layers of dielectric constant $\text{ε}_{1}$ and $\text{ε}_{2}$ and width $d_{1}$ and $d_{2}$ respectively. Variation of the potential and electric field with radial distance from $O$ is given. Select the correct one. (assume $V$ at $ \, r_{2}=0$ )

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Electric field
$\text{r} < \, \text{r}_{1}\text{, E }= \, 0$
$\mathrm{r}_1<\mathrm{r}<\mathrm{r}_1+\mathrm{d}, \mathrm{E}=\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{r}^2 \varepsilon_1}$
$\mathrm{r}_1+\mathrm{d}<\mathrm{r}<\mathrm{r}_2, \mathrm{E}=\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \varepsilon_2 \mathrm{r}^2}$
$\text{r }> \, \text{r}_{2}\text{, E}=0$
Potential can be find out by integrating
i.e. $\text{V}=-\displaystyle \int _{\in fty}^{r} \text{E.dr} = 0$