Question

11. A magnet of length L and moment M is cut into
two halves (A and B) perpendicular to its axis.
One piece A is bent into a semicircle of radius R
and is joined to the other piece at the poles as
shown in the figure below,
Assuming that the magnet is in the form of a
thin wire initially, the moment of the resulting
magnet is given by
1)M/2π
2)M/π
3)M(2+π)/2π
4)Mπ/2+π​

Answer 1

The correct option is,(3) M(2+π)/2π.

What do you mean by magnetic moment?

• A vector quantity that is a measure of the torque exerted on a magnetic system (such as a bar magnet or dipole) when placed in a magnetic field and that for a magnet is the product of the distance between its poles and the strength of either pole.

What is the SI unit of magnetic moment?

• Unit of magnetic moment is Weber.

According to the question:

After cutting, each piece has a magnetic moment of $\frac{M}{2} .$

But for the semicircular piece A,

$M_{A}=\frac{2\left(\frac{M}{2}\right) \sin \frac{180^{\circ}}{2}}{\pi}=\frac{M \sin 90^{\circ}}{\pi}\\ \Rightarrow M_{A}=\frac{M}{\pi}$

For the piece B, M$_{B}=\frac{M}{2}$

The resulting magnetic moment, $M_{R}=M_{A}+M_{B}$

$M_{R}=\frac{M}{\pi}+\frac{M}{2} \Rightarrow M_{R}=M\left[\frac{2+\pi}{2 \pi}\right]$

Hence, the moment of the resulting magnet are M(2+π)/2π.

Learn more about magnetic moment here,

https://brainly.in/question/13441014?msp_poc_exp=5

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