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 $10{-4}\, T$, 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 $(\mu_0 = 4\pi \times 10^{-7} NA^{- 2})$:

• 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\times10^{-7} \times i }{4\times10^{-2}} $
$ \therefore i = 20 A $