Question

Two particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB.  Assuming x<<d, show that this force is proportional to x.

Answer 1

 When x < < d:

\[F' = \frac{1}{2 \pi\epsilon_0}\frac{qQx}{\left( \frac{d}{2} \right)^3}      \left( \because x^2 < < \left( \frac{d}{2} \right)^2 \right)\] 

\[ \Rightarrow F' = \frac{4}{\pi\epsilon_0}\frac{qQx}{d^3}\]