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 $=\frac{{\mu }_0{i}_1{i}_2}{2\pi r}$