Question

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 $\vec{B} = B_0 \hat{j}$ as shown in the figure.The magnetic force on the wire if it has a current $i$ is:

• A. $-i B R \hat{j}$
• B. $2 i B R \hat{j}$
• C. $i B R \hat{j}$
• D. $-2 i B R \hat{j}$

Answer 1

Answer: (D)

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

Answer 2

The wire forms a semicircular arc with radius $R$ and length $l = 2R$.

Given that the direction of the magnetic field $\vec{B}$ is in the $+\hat{k}$ direction.

The magnetic force $\vec{F}$ is given by:

$\vec{F} = i \vec{l} \times \vec{B}$

Substituting the values:

$\vec{F} = -2iRB \hat{j}$