A magnetic wire of dipole moment $$4\pi$$ $$Am^2$$ is bent in the form of semi-circle. The new magnetic moment is?
Given:
The dipole moment of the wire is $$4\pi\ Am^2$$.
The Dipole moment of the wire is represented as:
$$M_i=mL$$
$$m=\dfrac{4\pi}{L}$$
Now, when the wire becomes a semicircle, the new magnetic moment will be:
$$M_f=mL'$$
The new distance between two poles is:
$$L'=2r\Rightarrow2\dfrac{L}{\pi}$$
So, new magnetic moment will be:
$$M_f=m\times\dfrac{2L}{\pi}$$
$$M_f=\dfrac{4\pi}{L}\times\dfrac{2L}{\pi}$$
$$=8\ Am^2$$
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