As shown in the figure, two infinitely long, identical wires are bent by $90^\circ$ and placed in such a way that the segments LP and QM are along the $x$-axis, while segments PS and QN are parallel to the $y$-axis. If $OP = OQ = 4$ cm, and the magnitude of the magnetic field at O is $10^{-4}$ T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($\mu_0 = 4\pi\times10^{-7}\ \text{N A}^{-2}$):
Answer: (A) $20$ A, perpendicular into the page
The parts LP and QM lie along the $x$-axis, whose line passes through O, so they give no field at O.
PS and QN are semi-infinite wires starting at the foot of the perpendicular from O, each at distance $d = 4$ cm:
$$B_1 = B_2 = \frac{\mu_0I}{4\pi d}$$
Current up along PS (left of O) and down along QN (right of O) both give a field into the page at O, so
$$B = \frac{2\mu_0I}{4\pi d} = \frac{2\times10^{-7}I}{0.04} = 5\times10^{-6}I = 10^{-4} \Rightarrow I = 20\ \text{A}$$
Solution by Sreeraj P, M.Sc Physics