Question

Two similar conductor spheres having charges +q and –q are placed at a separation 'd' from each other in air. The radius of each sphere is r and the separation between their centres is d (d >> r). Calculate the capacitance of the system

• A. $4\pi {\epsilon }_{0}r$
• B. $2\pi {\epsilon }_{0}r$
• C. $4\pi lo{g}_e\frac{{\epsilon }_{0}r}{d}$
• D. $4\pi lo{g}_e\frac{r}{d}$

Answer 1

The correct option is B

$2\pi {\epsilon }_{0}r$

Step-I

Give equal and opposite charges.

Step-II : $V_A-V_B=\frac{kq}{r}-(-\frac{kq}{r})=\frac{kq}{r}\times 2$

Step-III : $C=\frac{q}{V_A-V_B}=\frac{\frac{q}{q}}{2\pi {\epsilon }_{0}r}=2\pi {\epsilon }_{0}r$