Question

Find the magnetic induction at the point $O$. If the wire carrying a current $I=8.0A$ has the shape shown in the figure.

Answer 1

$I=8A$

To find -

Magnetic field at point O

${\overrightarrow{B}}_0={\overrightarrow{B}}_1+{\overrightarrow{B}}_2+{\overrightarrow{B}}_3$

${\overrightarrow{B}}_0=\frac{{\mu }_0}{4\pi }.\frac{i}{R}(-\hat{k})+\frac{{\mu }_0}{4}.\frac{i}{R}(-i)+\frac{{\mu }_0}{4\pi }\frac{i}{R}(-\hat{k})$

${\overrightarrow{B}}_0=-\frac{{\mu }_0}{4\pi }\frac{i}{R}[2\hat{k}+\pi \hat{i}]$

So $|{\overrightarrow{B}}_0|=\frac{{\mu }_0}{4\pi }.\frac{i}{R}\sqrt{{\pi }^2+4}$

Value of $R$ is not given in the question.