A wire of magnetic moment M is moulded accord | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the original length of the wire be $L$. The original magnetic moment is $M = m L$,where $m$ is the pole strength.The wire is bent into a quart

Vedclass · Accepted Answer

$\frac{2 \sqrt{2} M}{\pi}$

Vedclass · Answer

(C) Let the original length of the wire be $L$. The original magnetic moment is $M = m L$,where $m$ is the pole strength.The wire is bent into a quarter-circle arc of radius $R$. The length of this arc is $L = \frac{1}{4}(2 \pi R) = \frac{\pi R}{2}$.Thus,$m = \frac{M}{L} = \frac{M}{\pi R / 2} = \frac{2M}{\pi R}$.The new magnetic moment $M^{\prime}$ is the product of pole strength $m$ and the straight-line distance between the two ends of the arc (the chord length).The distance between the ends is $L^{\prime} = \sqrt{R^2 + R^2} = \sqrt{2} R$.Therefore,$M^{\prime} = m L^{\prime} = \left( \frac{2M}{\pi R} \right) (\sqrt{2} R) = \frac{2 \sqrt{2} M}{\pi}$.

$A$ wire of magnetic moment $M$ is moulded according to the figure. What is the new magnetic moment?

Similar Questions

Two identical thin bar magnets are placed mutually at right angles such that the north pole of one touches the south pole of the other. The length of each bar magnet is $\ell$. The magnitude of the resultant magnetic moment of the system is $[m = \text{pole strength of the magnet}]$.

The resultant magnetic moment of a neon atom will be

The intensity of magnetization of a bar magnet is $5.0 \times 10^{4} \text{ A m}^{-1}$. The magnetic length and the area of cross-section of the magnet are $12 \text{ cm}$ and $1 \text{ cm}^{2}$ respectively. The magnitude of the magnetic moment of this bar magnet is (in $SI$ unit):

Two points $A$ and $B$ are situated at a distance $x$ and $2x$ respectively from the nearer pole of a magnet $2 \ cm$ long. The ratio of the magnetic field at $A$ and $B$ is

If a bar magnet of pole strength $m$ and magnetic moment $M$ is cut equally $5$ times parallel to its axis and again $3$ times perpendicular to its axis, then the pole strength and magnetic moment of each piece are respectively

Vedclass Test Series

Exam Paper Generator

Online Exam Module