Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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

3M/\pi

2M/\pi

M/2

Original Magnetic Moment: The magnetic dipole moment ( $M$ ) of a bar magnet is the product of its pole strength ( $m$ ) and its length ( $L$ ). $M = m \times L$
Bent Magnet Geometry: When the magnet is bent into an arc, the length of the arc remains $L$ . Let the radius of the arc be $R$ and the angle subtended at the center be $\theta$ (in radians). $L = R\theta \implies R = \frac{L}{\theta}$
New Magnetic Moment ( $M'$ ): The new magnetic moment is the product of the pole strength ( $m$ ) and the straight-line distance (chord) between the two poles. The chord length is given by $2R \sin(\theta/2)$ . $M' = m \times (2R \sin(\theta/2))$
Substitution: Substituting $R = L/\theta$ : $M' = m \times 2 \left( \frac{L}{\theta} \right) \sin(\theta/2) = \frac{2(mL)}{\theta} \sin(\theta/2) = \frac{2M}{\theta} \sin(\theta/2)$
Determining the Angle: Based on the probable answer $3M/\pi$ , we test the angle $\theta = 60^\circ = \pi/3$ radians. $M' = \frac{2M}{\pi/3} \sin(60^\circ/2) = \frac{6M}{\pi} \sin(30^\circ)$ $M' = \frac{6M}{\pi} \times \frac{1}{2} = \frac{3M}{\pi}$ This confirms the magnet is bent into an arc subtending $60^\circ$ at the center.

Practice Mode Available

Join thousands of students and practice with AI-generated mock tests.