An iron bar of length $L$ has a magnetic moment $M$. It is bent at the middle of its length such that the two

Question

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:

Accepted Answer

1. **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 ($L$).
   $$ M = m 	imes L $$
2. **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 $60^{\circ}$.
3. **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:
   $$ L' = L/2 $$
4. **Calculate New Magnetic Moment:**
   $$ M' = m 	imes L' = m 	imes (L/2) = \frac{1}{2} (mL) = \frac{M}{2} $$
   (This application of calculating displacement is supported by the vector concepts in the source , ).

Step-by-Step Solution

Practice All PHYSICS Questions