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

• A. $40\text{A}$ perpendicular into the page
• B. $20\text{A}$ perpendicular into the page
• C. $20\text{A}$ perpendicular out of the page
• D. $40\text{A}$ perpendicular out of the page

Answer 1

The correct option is B $20\text{A}$ perpendicular into the page

Let $I$ be the current in each wire, (directed inwards) Magnetic field at ${}^{\prime }{O}^{\prime }$ due to $LP$ and $QM$ will be zero.
$i.e.B_0=B_{PS}+B_{QN}$

$\therefore \text{Net magnetic field}{B}_0=\frac{{\mu }_{0}i}{4\pi d}+\frac{{\mu }_{0}i}{4\pi d}$

or ${10}^{-4}=\frac{2{\mu }_{0}i}{4\pi d}=\frac{2\times {10}^{-7}\times i}{4\times {10}^{-2}}$

$\therefore i=20\text{A}$ and the direction of magnetic field is perpendicular into the plane