Question

A system of three charges are placed as shown in the figure :
If D >> d, the potential energy of the system is best given by :

• A. $\frac{1}{4 \pi in_0} \bigg[ - \frac{q^2}{d} - \frac{qQd}{2D^2}\bigg]$
• B. $\frac{1}{4 \pi in_0} \bigg[ + \frac{q^2}{d} + \frac{qQd}{D^2}\bigg]$
• C. $\frac{1}{4 \pi in_0} \bigg[ - \frac{q^2}{d} + \frac{qQd}{D^2}\bigg]$
• D. $\frac{1}{4 \pi in_0} \bigg[ - \frac{q^2}{d} - \frac{qQd}{D^2}\bigg]$

Answer 1

Answer: (D)

U$_{total} = U_{self \, of \, dipole} + U_{interaction}$
= $- \frac{kq^2}{d} - \bigg( \frac{kQ}{D^2}\bigg) qd$
= $- k \bigg[ - \frac{q^2}{d} + \frac{qQd}{D^2} \bigg]$