Question

If the circumference of a sphere is 2m, then capacitance of sphere in water would be

• A. 2700 pF
• B. 2760 pF
• C. 2780 pF
• D. 2800 pF

Answer 1

The correct option is D 2800 pF

Capacitance is given as

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

For a sphere placed in water, the capacitance will be

$\text{C}=4\pi \epsilon \text{R}$

Here, $\epsilon$ is the permittivity of water.

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

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

Where, $k$ (relative permittivity) $=\frac{\epsilon }{{\epsilon }_o}=79.1at{35}^{o}C$

Circumference, $2\pi R=2m$

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

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

$\text{C}=4\times 8.85\times 0^{-12}\times 79.1$

$\text{C}=2800\times {10}^{-12}\text{F}$

$\text{C}=2800\text{pF}$

Hence, capacitance is $2800pF$