Q: Two long wires carrying current I_{1} and I_{2} are arranged as shown in figure. the one carrying current I_{1} is along is the x-axis. The other carrying current I_{2} is along a line parallel to the y-axis given by x = 0 and z = d. Find the force exerted at O2 because of the wire along the x-axis.

Solution : Magnetic field at O2 due to wire carrying current I_{1} is

$\displaystyle B = \frac{\mu_0}{4 \pi} frac{2 I_1}{d}$ , and direction is $\hat{-j}$

$\displaystyle B = \frac{\mu_0}{2 \pi} frac{I_1}{d}$

Force acting on wire carrying current I_{2} will be

$\displaystyle \vec{F} = I_2 (\vec{l} \times \vec{B})$

The angle between $\vec{l}$ and $\vec{B}$ is 180° because it is anti parallel .

Hence force exerted at O_{2} because of the wire along the x-axis is Zero .