Question 74: Magnetism and Matter

Question

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 $B=B_0 \hat{k}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is:
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lseghbhv/39180403-d934-45f8-8828-aa906dfefe20/195c8c30-c72f-11ee-8cb5-7deab4010c9e/file-6y3zli1lseghbhw.png?format=png)

Accepted Answer

Note : Direction of magnetic field is in $+\hat{k}$
$\begin{aligned}
& \overrightarrow{\mathrm{F}}=\mathrm{i} \vec{\ell} 	imes \overrightarrow{\mathrm{B}} \
& \ell=2 \mathrm{R} \
& \overrightarrow{\mathrm{F}}=-2 \mathrm{iRB} \hat{\mathrm{j}}
\end{aligned}$
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsludpk4/453b8c51-df9f-4c63-8827-ba1780cacc92/f1578640-cb3e-11ee-ad47-a16d1086e690/file-6y3zli1lsludpk5.png?format=png)

Answer

$i B R \hat{j}$

Answer

$-2 i B R \hat{j}$

Answer

$2 i B R \hat{j}$

Answer

$-i B R \hat{j}$

Magnetism and Matter

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{k} as shown in figure. The magnetic force on the wire if it has a current i is:

Choose the correct answer: