A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field as shown in the figure. The magnetic force on the wire if it has a current i is

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Solution

Q.
A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_{0} \hat{j}$ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

1 $- 2 i B R \hat{j}$

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

3 $- i B R \hat{j}$

4 $i B R \hat{j}$

Ans.
(1)

Note: Direction of magnetic field is in $+ \hat{k}$

Force on current carrying wire,

$\vec{F} = i \vec{ℓ} \times \vec{B}$

Here, $ℓ = 2 R$

$\Rightarrow \vec{F} = - 2 i R B \hat{j}$

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