Question

As shown in the figure, two infinitely long, identical wires are bent by$90$ 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 ($\mu 0=4\pi {10}^{7}NA2$)

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

Answer 1

The correct option is D $20A$, perpendicular into the page

Magnetic field at ${}^{\prime }{O}^{\prime }$ will be done to 'PS' and ${}^{\prime }Q{N}^{\prime }$ only
i.e $B_0=B_{PS}+B_{QN}\to$ Both inwards
Let current in each wire $=i$
$\therefore B_0=\frac{{\mu }_{0}i}{4\pi d}+\frac{{\mu }_{0}i}{4\pi d}$
$\therefore i=20A$