Question

If the maximum circumference of a sphere is $2m$. Then its capacitance in water would be: (Dielectric constant of water $=81$)

• A. $2867pF$
• B. $2385pF$
• C. $236.5pF$
• D. $2865pF$

Answer 1

The correct option is A $2867pF$

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

For sphere in water $C=4\pi \epsilon R$ where $\epsilon$ is the permittivity of water.

$\because K=\frac{\epsilon }{{\epsilon }_0}$

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

It is given that circumference = 2 m

$2=2\pi R$

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

So, capacitance

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

$=4{\epsilon }_{0}K$

$=4\times 8.85\times {10}^{-12}\times 81$

$=2867.4\times {10}^{-12}$

$=2867.4pF$