Question

A rigid wire consists of a semi-circular portion of radius R and two straight sections (figure). The wire is partially immersed in a perpendicular magnetic field B, as shown in the figure. Find the magnetic force on the wire if it carries a current i.
Figure

Answer 1

If the wire carries current i, the magnetic force is i2RB.

Explanation:

It is given that

The rigid wire, the semi-circular portion’s radius = R  

        Magnetic field = B

        Electric current = i

• As given in the scenario, the wire is partly absorbed in a magnetic field that is perpendicular.
• RS and PQ are the straight wires with length l . It is to be noted that the magnetic field of both the wires are same. On these wires, the force will be equivalent in magnitude, but they have opposite directions to each other.
• Thus, on the wire PQ, the magnetic force and the force on wire RS are the same, but opposite to one another. So, both the forces are cancelled.
• So, PR, the only semi-circular loop will involve a net magnetic force.
• Now, angle between the magnetic field and the length of the wire, $\vartheta=90 E \check{S}$
• In the loop PR, the magnetic force,  F →= il→×B→

        Here, l = 2R

        F→ = i2RB