Electrostatics Question 657
Question: Two infinitely long parallel wires having linear charge densities $ {\lambda _{1}} $ and $ {\lambda _{2}} $ respectively are placed at a distance of $ R $ metres. The force per unit length on either wire will be $ ( k=\frac{1}{4\pi {\varepsilon _{0}}} ) $
Options:
A) $ k\frac{2{\lambda _{1}}{\lambda _{2}}}{R^{2}} $
B) $ k\frac{2{\lambda _{1}}{\lambda _{2}}}{{{R}^{{}}}} $
C) $ k\frac{{\lambda _{1}}{\lambda _{2}}}{R^{2}} $
D) $ k\frac{{\lambda _{1}}{\lambda _{2}}}{R} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Force on l length of the wire 2 is $ F _{2}=QE _{1}=({\lambda _{2}}l)\frac{2k{\lambda _{1}}}{R} $
$ \Rightarrow \frac{F _{2}}{l}=\frac{2k{\lambda _{1}}{\lambda _{2}}}{R} $ Also $ \frac{F _{2}}{l}=\frac{F _{2}}{l}=\frac{F}{l}=\frac{2k{\lambda _{1}}{\lambda _{2}}}{R} $
