Physics - Magnetism Question with Solution | TestHub

For a current flowing into a circular arc, the magnetic induction at the centre is

$\text{B}=\left(\frac{{\mu }_{0}i}{4\pi }\right)\mathrm{ \theta }$

or$\text{B}\propto \mathrm{i}\mathrm{\theta }$

In the given problem, the total current is divided into two arcs

$\mathrm{i}\propto \frac{1}{\text{resistance of arc}}$

$\propto \frac{1}{\text{length of arc}}$

$\propto \frac{1}{\text{angle subtended at centre }\left(\theta \right)}$





or$\text{i}\mathrm{\theta }=\text{constant}$

i.e., magnetic field at centre due to arc$\mathrm{AB}$is equal and opposite to the magnetic field at centre due to arc$\mathrm{ACB}$. Or the net magnetic field at the centre is zero.