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. 4πε₀r
• B. 2πε₀r
• C. 4πlog_e
• D. 4πlog_e

Answer 1

Answer: (B)

2πε₀r

Answer 2

Step-I

Give equal and opposite charges.

Step-II : V_A – V_B =$\frac { \mathrm { kq } } { \mathrm { r } }$ –=$\frac { \mathrm { kq } } { \mathrm { r } }$× 2

Step-III : C == $\frac { \mathrm { q } } { \frac { \mathrm { q } } { 2 \pi \varepsilon _ { 0 } \mathrm { r } } }$ = 2πε₀r