Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

An iron bar of length $L$ has a magnetic moment $M$ . It is bent at the middle of its length such that the two arms make an angle $60^{\circ}$ with each other. The magnetic moment of this new magnet is:

M/2

M\sqrt{3}

Step-by-Step Solution

Definition of Magnetic Moment: The magnetic moment ( $M$ ) of a bar magnet is the product of its pole strength ( $m$ ) and the straight-line distance (vector displacement) between its poles ( $L$ ). $M = m \times L$
Geometry of the Bent Magnet: The bar is bent at the middle, creating two arms of length $L/2$ each. The angle between these arms is $60^{\circ}$ .
Calculate New Effective Length: The new magnetic moment ( $M'$ ) depends on the shortest distance between the two ends (poles) of the bent magnet. The two arms and the line connecting the poles form a triangle. Since the two arms are equal ( $L/2$ ) and the included angle is $60^{\circ}$ , the triangle is equilateral. Therefore, the new distance between the poles ( $L'$ ) is equal to the length of an arm: $L' = L/2$
Calculate New Magnetic Moment: $M' = m \times L' = m \times (L/2) = \frac{1}{2} (mL) = \frac{M}{2}$ (This application of calculating displacement is supported by the vector concepts in the source , ).

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