Question

If an external uniform magnetic field $B_o\hat{j}$ is applied, determine the force ${\overrightarrow{F}}_1$ and ${\overrightarrow{F}}_2$ on the semicircles KLM and KNM due to the field and the net force $\overrightarrow{F}$ on the loop.

Answer 1

In uniform magnetic field,

${\overrightarrow{F}}_{KLM}={\overrightarrow{F}}_{KNM}={\overrightarrow{F}}_{KM}$

$=I(\overrightarrow{I}\times \overrightarrow{B})$

$=I\left[2R\right(-\hat{k})\times B_0\hat{j}]$

$=\left(2B_{0}IR\right)\hat{i}$

Therefore net force is two times the above value.