Physics - Magnetism Question with Solution | TestHub

Magnetic field due to a circular loop at the centre of the loop is $B_1=\frac{{\mu }_0}{4\pi }\frac{2\pi I_c}{R}$. Magnetic field due to a straight line at the centre of the loop is $B_2=\frac{{\mu }_{0}2I_e}{4\pi H}$ Both these fields act in opposite direction hence total magnetic field at the centre of the loop is $$\begin{array}{rl}& B=B_1-B_2=\frac{{\mu }_{0}2\pi I_c}{4\pi R}-\frac{{\mu }_{0}2I_e}{4\pi H}\\ & B=0\text{ (given). }\\ & \therefore \frac{{\mu }_{0}2\pi I_c}{4\pi R}=\frac{{\mu }_{0}2I_e}{4\pi H}\text{ or, }H=\frac{I_{e}R}{\pi I_c}.\end{array}$$