question_answer

Two long straight wires are placed on a smooth horizontal table. Wires have equal but opposite charges. Magnitude of linear charge density on each wire is\[\lambda \]. For unit length of wires, the work required to increase the separation between the wires from a to 2a.

A) \[\frac{{{\lambda }^{2}}}{2\pi {{\in }_{0}}}\ell n2\]     

B)        \[\frac{\lambda }{2\pi {{\in }_{0}}}\ell n2\]

C) \[\frac{\lambda }{2\pi {{\in }_{0}}}\]     

D)        \[\frac{{{\lambda }^{2}}}{2\pi {{\in }_{0}}a}\]

Correct Answer: A

Solution :

[a] \[F=\lambda E\] \[W=\int\limits_{a}^{2a}{(\lambda E)dr}=\int\limits_{a}^{2a}{\frac{{{\lambda }^{2}}dr}{2\pi {{\in }_{0}}r}}\]