Question

A semicircular wire of radius $r,$ carrying a current $i,$ is placed in a magnetic field of magnitude $B$. The force acting on it :

• A. can never be zero
• B. can have the maximum magnitude $2Bir$
• C. can have the maximum magnitude $Bi\mu r$
• D. can have the maximum magnitude $Bir$

Answer 1

The correct option is B can have the maximum magnitude $2Bir$

Magnetic force on the semicircular wire,
$\overrightarrow{F_{mag}}=i\int (\overrightarrow{dl}\times \overrightarrow{B})=iB\int \overrightarrow{dl}=iB\left(2r\right)=2iBr(-\hat{r})$ where $r$ is the radius of the semi circular loop.