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
$r<r_1,E=0$
$r_1<r<r_1+d,E=\frac{Q}{4\pi {\epsilon }_0{r}^2{\epsilon }_1}$
$r_1+d<r<r_2,E=\frac{Q}{4\pi {\epsilon }_0{\epsilon }_2{r}^2}$
$r>r_2,E=0$
Potential can be find out by integrating
i.e. $V=-E.dr$