Question

If the circumferences of a sphere is $2m$, then capacitance of sphere in water would be:

• A. $2700pF$
• B. $2760pF$
• C. $2780pF$
• D. $2846pF$

Answer 1

The correct option is D $2846pF$

Capacitance is given as

$C={\epsilon }_0\frac{A}{d}$

For a sphere placed in water, the capacitance will be,

$C=4\pi \epsilon R$

Here, $\epsilon$ os the permittivity of water

In terms of permittivity of free space and dielectric constant of water, we get

$C=4\pi {\epsilon }_{0}kR$

It is given that circumference is 2m

Hence, $c=2\pi R$

$\therefore R=\frac{1}{\pi }$

$C=4\pi {\epsilon }_{0}k\frac{1}{\pi }=4{\epsilon }_{0}k$

$C=4\times 8.85\times {10}^{-12}\times 80.4$

$C=2846\times {10}^{-12}F$

$C=2846pF$