Question

A straight steel wire of length 'l' has a magnetic moment 'M'. It is bent into various shapes shown in figure. Find out new magnetic moment of each shape.

Answer 1

For shape (a): New magnetic moment is $\frac{M}{\sqrt{2}}$. For shape (b): New magnetic moment is $0$.

Answer 2

For shape (a), the wire is bent into two segments of length $l/2$ each, forming a right angle. The magnetic moment of each segment is $M/2$. The resultant magnetic moment is the vector sum: $\sqrt{(M/2)^2 + (M/2)^2} = M/\sqrt{2}$.

For shape (b), the wire of length 'l' is bent into an equilateral triangle. Each side has length $l/3$, and each segment has magnetic moment $M/3$. The vector sum of these three moments, oriented along the sides of an equilateral triangle, results in a net magnetic moment of zero due to symmetry.