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 $
$r _1< r < r _1+ d , E =\frac{ Q }{4 \pi \varepsilon_0 r ^2 \varepsilon_1}$
$ r _1+ d < r < r _2, E =\frac{ Q }{4 \pi \varepsilon_0 \varepsilon_2 r ^2} $
$ r>r_2, E=0 $
Potential can be find out by integrating
i.e. $V =- E . dr$