Question

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 $OP=OQ=4cm$, and the magnitude of the magnetic field at $O$ is $10-4T$, 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 $({\mu }_0=4\pi \times 10^{-7}N{A}^{-2})$:

• A. 40 A, perpendicular into the page
• B. 40 A, perpendicular out of the page
• C. 20 A, perpendicular out of the page
• D. 20 A, perpendicular into the page

Answer 1

Answer: (D)

Magnetic field at ‘O’ will be done to ‘PS’ and ‘QN’ only
i.e. $B_0=B_{PS}+B_{QN}\to$ Both inwards
Let current in each wire = i
$\therefore B_0=\frac{{\mu }_{0}i}{4\pi d}+\frac{{\mu }_{0}i}{4\pi d}$
or $10^{-4}=\frac{{\mu }_{0}i}{2\pi d}=\frac{2\times 10^{-7}\times i}{4\times 10^{-2}}$
$\therefore i=20A$