Question

The earth has volume V and surface area A, then capacitance would be

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Volume of sphere (earth) $=\frac{4}{3}\pi R^3$ where R is the radius of the sphere. Area of the sphere $=4\pi R^2$ Now, $\frac{V}{A}=\frac{R}{3}$ ???(i) Capacitance of a sphere $C=4\pi {\epsilon }_{0}R$ ?...(ii) From Eqs. (i) and (ii), we get $C=4\pi {\epsilon }_0\left(\frac{3V}{A}\right)=\frac{12\pi {\epsilon }_{0}V}{A}$