Question

The radius of the circular plates of a parallel plate condenser is $r$. Air is there as the dielectric. The distance between the plates if its capacitance is equal to that of an isolated sphere of radius $r^{\prime }$ is :

• A. $\frac{r^2}{4r^{\prime }}$
• B. $\frac{r^2}{r^{\prime }}$
• C. $\frac{r}{r^{\prime }}$
• D. $\frac{r^2}{4}$

Answer 1

The correct option is A $\frac{r^2}{4r^{\prime }}$

We know capacitance of sphere,

$\Rightarrow C_1=4\pi {ϵ}_{\circ }{r}^{\prime }$

We know capacitance of a parallel plate capacitor $C_2=\frac{{ϵ}_{0}A}{d}$ for parallel plate capacitor

$\Rightarrow C_2=\frac{{ϵ}_0\pi r^2}{d}$

given $C_1=C_2$

$\frac{{ϵ}_0\pi r^2}{d}=4\pi {ϵ}_{\circ }{r}^{\prime }$

$\Rightarrow d=\frac{r^2}{4r^{{}^{\prime }}}$