An infinite straight conductor is kept along $\displaystyle \mathrm{X}^{\prime} \mathrm{X}$ axis and carries a current I. A charge $\displaystyle q$ at point $\displaystyle P(0, \mathrm{r})$ starts moving with velocity $\displaystyle \vec{v}=v_{0} \hat{j}$ as shown in figure. Find the direction and magnitude of force initially experienced by the charge.

Magnetic field at P due to infinite straight conductor carrying current: $\displaystyle \vec{B}=\frac{\mu_{0} I}{2 \pi r} \hat{k}$ Force on charge q in this magnetic field: $\displaystyle \vec{F}=q(\vec{v} \times \vec{B})$ $\displaystyle \vec{F}=q\left[\left(v_{0} \hat{j}\right) \times\left(\frac{\mu_{0} I}{2 \pi r}\right) \hat{k}\right]$ $\displaystyle \vec{F}=\frac{\mu_{0} q v_{0} I}{2 \pi r} \hat{i}$ The magnitude of force $\displaystyle F=\frac{\mu_{0} q v_{0} I}{2 \pi r}$ The direction of force on the charge is along the +ve X-axis.