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 j ˆ as shown in figure. The magnetic force on the wire if it has a current i is :
Select the correct option:
A
$-\mathrm{iBR} \hat{\jmath}$
B
$2 \mathrm{iBR} \hat{\jmath}$
C
$i B R \hat{j}$
D
$-2 \mathrm{iBR} \hat{j}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol.
Note : Direction of magnetic field is in $+\hat{k}$
$$
\begin{aligned}
& \overrightarrow{\mathrm{F}}=\mathrm{i} \vec{\ell} \times \overrightarrow{\mathrm{B}} \\
& \ell=2 \mathrm{R} \\
& \vec{F}=-2 i R B \hat{i}
\end{aligned}
$$
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