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 $i_2$ respectively. The force experienced by each of the straight wires is ( r is the distance of their separation)

• A. repulsive and equal to$\left({\mu }_0/2\pi \right)\left(i_1{i}_{2}l/r\right)$
• B. attractive and equal to$\left({\mu }_0/2\pi \right)\left(i_1{i}_2{l}^2/r\right)$
• C. repulsive and equal to$\left({\mu }_0/2\pi \right)\left(i_1{i}_2{l}^2/r\right)$
• D. attractive and equal to$\left({\mu }_0/2\pi \right)\left(i_1{i}_{2}l/r\right)$

Answer 1

Answer: (A)

repulsive and equal to$\left({\mu }_0/2\pi \right)\left(i_1{i}_{2}l/r\right)$

The flux density(B) due to current($i_1$) carrying conductor at distance r from it is

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

the force experienced due to another conductor (of same length) per unit length carrying current $i_2$ is

$F=B{i}_2$

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

since both conductors are of same length l, we get

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