JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Magnetic Effects of Current

Each long straight wire produces a field of size $B=\frac{{\mu }_{0}I}{2\pi d}$ at P, which is a perpendicular distance $d$ from each. By the right-hand rule the wire along the x-axis (current in $+\hat{x}$) gives a field at P pointing into the page, $-\hat{k}$, while the wire along the y-axis (current in $+\hat{y}$) gives a field out of the page, $+\hat{k}$. The wires are equidistant from P and carry equal currents, so the two contributions are equal in size and opposite in direction; they cancel, and the net magnetic field at P is zero.