Question

A wire AB, in the shape of two semicircular segments of radius \( R \) each and carrying a current \( I \), is placed in a uniform magnetic field \( B \) directed into the page (see figure). The magnitude of the force due to the field on the wire AB is

• A. zero
• B. \( 4IBR \)
• C. \( 2 \pi RIB \)
• D. \( 2 \, I \, R \, B \)

Hint:

For a current-carrying wire in a magnetic field, the force is proportional to the length of the wire and the magnetic field strength.

Answer 1

The Correct Option is D

Step 1: Analyzing the force on the wire.
For a wire carrying a current in a magnetic field, the force on the wire is given by: \[ F = I L B \sin \theta \] where \( L \) is the length of the wire and \( \theta \) is the angle between the wire and the magnetic field. In this case, the total force is calculated by considering the semi-circular segments of the wire.

Step 2: Conclusion.
Thus, the correct answer is option (D).

Final Answer: \[ \boxed{2IRB} \]