A circular loop of radius $\displaystyle 10$ cm carrying current of $\displaystyle 1.0$ A lies in $\displaystyle x-\mathrm{y}$ plane. A long straight wire lies in the same plane parallel to $\displaystyle x$-axis at a distance of $\displaystyle 20$ cm as shown in figure. Find the direction and value of current that has to be maintained in the wire so that the net magnetic field at O is zero.

Magnetic field due to circular current loop at its centre O: $\displaystyle B_{1}=\frac{\mu_{0} I_{1}}{2 r}$ $\displaystyle =\frac{\mu_{0} \times 1}{2 \times 0.1}$ $\displaystyle =5 \mu_{0} \mathrm{~T}$ The magnetic field $\displaystyle B_{1}$ is perpendicular to the plane of the loop and directed inwards. Magnetic field due to long current carrying straight wire at O: $\displaystyle B_{2}=\frac{\mu_{0} I_{2}}{2 \pi r}$ $\displaystyle B_{2}=\frac{\mu_{0} I_{2}}{2 \pi \times 0.2} \mathrm{~T}$ For the net magnetic field at O to be zero, $\displaystyle B_{1}$ should be equal and opposite to $\displaystyle B_{2}$: $\displaystyle 5 \mu_{0}=\frac{\mu_{0} I_{2}}{0.4 \pi}$ $\displaystyle I_{2}=2 \pi \mathrm{~A}$ $\displaystyle =6.28 \mathrm{~A}$ Direction of current in the straight wire is along the +ve x axis.