A bar magnet of length l and magnetic dipole | vedclass

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

Question

(B) Let $m$ be the pole strength of each pole of the bar magnet of length $l$. Then,the initial magnetic dipole moment is given by:$M = m 	imes l$ ..

Vedclass · Accepted Answer

$\frac{3}{\pi} M$

Vedclass · Answer

(B) Let $m$ be the pole strength of each pole of the bar magnet of length $l$. Then,the initial magnetic dipole moment is given by:$M = m 	imes l$ ......... $(i)$When the bar magnet is bent into an arc of radius $r$ subtending an angle $	heta = 60^{\circ} = \frac{\pi}{3} 	ext{ radians}$ at the center,the arc length $l$ is:$l = r 	heta = r 	imes \frac{\pi}{3}$$r = \frac{3l}{\pi}$The new magnetic dipole moment $M^{\prime}$ is the product of pole strength $m$ and the straight-line distance (chord length) between the two poles.The chord length $d$ is given by $2r \sin(\frac{	heta}{2}) = 2r \sin(30^{\circ}) = 2r 	imes \frac{1}{2} = r$.Thus,$M^{\prime} = m 	imes d = m 	imes r$.Substituting $r = \frac{3l}{\pi}$:$M^{\prime} = m 	imes \frac{3l}{\pi} = \frac{3}{\pi} (m 	imes l) = \frac{3}{\pi} M$ (using equation $(i)$).

$A$ bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be

Similar Questions

$A$ magnetized wire of magnetic moment $M$ and length $l$ is bent in the form of a semicircle of radius $r$. Then its new magnetic moment is:

What does the analogy of a bar magnet's and a solenoid's magnetic field lines suggest?

If $L$ is the length of a bar magnet,then the separation between the two poles is nearly

Magnetic dipole moment is a

$A$ steel wire of length $l$ and magnetic moment $M$ is bent into a semicircular arc of radius $R$. The new magnetic moment is

Vedclass Test Series

Exam Paper Generator

Online Exam Module