Question

An arc of a circular loop of radius $R$ is kept in the horizontal plane and a constant magnetic field $B$ is applied in the vertical direction as shown in the figure. If the arc carries current $I$ then find the force on the arc.

• A. $IRB$
• B. $\frac{\text{IRB}}{4}$
• C. $\sqrt{2}IRB$
• D. $\frac{\text{IRB}}{\sqrt{2}}$

Answer 1

Answer: (C)

If this loop is close net force on it will be zero
so F + F_straight = 0
$\Rightarrow \text{F}=-{\text{F}}_{\text{straight}}$
$\text{F}=\text{I}\sqrt{2}\text{RB}$
$\text{F}=\sqrt{2}IRB$