Question 196 of 276

A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B={B}_{0}\hat{j}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is :

A$-iBR\hat{j}$B$2iBR\hat{j}$C$iBR\hat{j}$D$-2iBR\hat{j}$

Show answer and solution▾

Answer: (D) $-2iBR\hat{j}$

Direction of magnetic field is in $+\hat{k}$
Force acting on wire is given by, $\vec{F}=i\left(\vec{l}\times \vec{B}\right)$
As, $l=2R$, we get
$\Rightarrow \vec{F}=-2iRB\hat{j}$