Question

A wire bent as shown in figure carries a current $i$ and is placed in a uniform field of magnetic induction $\overrightarrow{B}$ that emerges out from the plane of the figure.The magnetic force acting on the wire is:

• A. $2BIR$
• B. $4BIR$
• C. $BIR$
• D. $\frac{5}{2}BIR$

Answer 1

The correct option is B $4BIR$

The given wire is composed of two straight sections and one semi-circular section.

The effective length vector $\overrightarrow{L}$ of wire is shown below:


$|\overrightarrow{L}|=R+2R+R=4R$
Since, the angle between $\overrightarrow{L}\&\overrightarrow{B}$ is ${90}^{\circ }$, using relation for magnetic force:

$F=iLB\sin \theta$

$F=i\left(4R\right)B\sin {90}^{\circ }$

$\therefore F=4BIR$