Question

Two long straight wires of length l lie parallel to one another and carry currents opposite to one another of magnitudes i-1 and i2 respectively. The force experienced by each of the straight wires is: (r is their distance of separation)

• A. repulsive and equal to $ \frac{{{\mu }_{0}}}{2\pi }\,\frac{{{l}^{2}}{{i}_{1}}{{i}_{2}}}{r} $
• B. repulsive and equal to $ \frac{{{\mu }_{0}}}{2\pi }\,\frac{l{{i}_{1}}{{i}_{2}}}{r} $
• C. attractive and equal to $ \frac{{{\mu }_{0}}{{l}^{2}}{{i}_{1}}{{i}_{2}}}{2\pi {{r}^{2}}} $
• D. attractive and equal to $ \frac{{{\mu }_{0}}l{{i}_{1}}{{i}_{2}}}{2\pi r} $

Answer 1

Answer: (B)

The force per unit length on either wire is given by
$ F=\frac{{{\mu }_{0}}{{i}_{l}}.{{i}_{2}}}{2\pi r} $ Total force $ F=\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}_{1}}{{i}_{2}}l}{r} $ When the current is flowing in the parallel wires in opposite direction, then the force will be repulsive which will be equal to $ =\frac{{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{2\pi r} $