question_answer

A point charge q is situated at a distance d from one end of a thin non-conducting rod of length L having a charge Q distributed uniformly along its length. The magnitude of the electric force between them will be -

A) \[\frac{1}{4\pi {{\in }_{0}}}\frac{qQ}{d(d+L)}\]

B) \[\frac{qQ}{4\pi {{\in }_{0}}d}\]

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

D) \[\frac{qQ}{8\pi {{\in }_{0}}d(d+L)}\]

Correct Answer: A

Solution :

[a] \[dF=\frac{kqdQ}{{{x}^{2}}}=\frac{kq}{{{x}^{2}}}\frac{Q}{L}dx\] \[F=\int\limits_{x=d}^{x=d+L}{dF}\]