Two long insulated straight wires carrying currents of $\displaystyle 3$ A and $\displaystyle 5$ A are arranged in XY plane as shown in figure. Find the magnitude and direction of the net magnetic fields at points $\displaystyle P_1(2\mathrm{m}, 2\mathrm{m})$ and $\displaystyle P_2(-1\mathrm{m}, 1\mathrm{m})$.

Net magnetic field at point $\displaystyle P_{1}$: $\displaystyle B=B_{y(\text {wire})}-B_{x(\text {wire})}$ $\displaystyle =\frac{\mu_{0} I_{1}}{2 \pi r}-\frac{\mu_{0} I_{2}}{2 \pi r}$ $\displaystyle =\frac{\mu_{0}}{2 \pi \times 2}(5-3)$ $\displaystyle B=2 \times 10^{-7} \mathrm{~T}$ The direction of the net magnetic field is along the $\displaystyle -$ve z-axis. Net magnetic field at point $\displaystyle P_{2}$: $\displaystyle B=B_{y(\text {wire})}+B_{x(\text {wire})}$ $\displaystyle =\frac{\mu_{0} I_{1}}{2 \pi r}+\frac{\mu_{0} I_{2}}{2 \pi r}$ $\displaystyle =\frac{\mu_{0}}{2 \pi \times 1}(5+3)$ $\displaystyle =\frac{4 \mu_{0}}{\pi}$ $\displaystyle =16 \times 10^{-7} \mathrm{~T}$ The direction of the net magnetic field is along the $\displaystyle +$ve z-axis.