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

The Correct Option is D

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:

\[ \vec{F} = -2iRB \hat{j} \]