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. $\frac{1}{4Ï€i{n}_0}[−\frac{q^2}{d}−\frac{qQd}{2D^2}]$
• B. $\frac{1}{4Ï€i{n}_0}[+\frac{q^2}{d}+\frac{qQd}{D^2}]$
• C. $\frac{1}{4Ï€i{n}_0}[−\frac{q^2}{d}+\frac{qQd}{D^2}]$
• D. $\frac{1}{4Ï€i{n}_0}[−\frac{q^2}{d}−\frac{qQd}{D^2}]$

Answer 1

Answer: (D)

U${}_{total}=U_{selfofdipole}+U_{interaction}$
= $−\frac{k{q}^2}{d}−\left(\frac{kQ}{D^2}\right)qd$
= $−k[−\frac{q^2}{d}+\frac{qQd}{D^2}]$