Question

A circular loop which is in the form of a major arc of a circle is kept in the horizontal plane and a constant magnetic field B is applied in the vertical direction such that the magnetic lines of forces go into the plane. If R is the radius of the circle and it carries a current I in the clockwise direction then the force on the loop will be.

• A. BIR $\tan \alpha$
• B. $2$ BIR $\cos \left(\alpha /2\right)$
• C. $2$ BIR $\sin \left(\alpha /2\right)$
• D. none of these

Answer 1

The correct option is C $2$ BIR $\sin \left(\alpha /2\right)$

Force due to the section ${AA}^1$ and ${BB}^1$ is same and opposite.

Hence net force due to these section is zero.

Force due to section $A^1{B}^1$ is F

Length of $A^{1}D{B}^1=2A^{1}D=2R\sin \frac{\alpha }{2}$

$F=\varphi i\mu \times \overrightarrow{B}=i\left(A^{1}D{B}^1\right)\overrightarrow{B}=2iRB\sin \frac{\alpha }{2}$

Downward direction.

Answer is (option - C).