Question

A steel wire of length l has a magnetic moment M. it is then bent into a semicircular arc. the new magnetic moment is

• A. M
• B. $2M{\pi }^{-}1$
• C. M/l
• D. $M\times I$

Answer 1

The correct option is B $2M{\pi }^{-}1$

$\text{Given}$: Length l and magnetic moment M of steel wire

$\text{To find}$: New magnetic moment

$\text{Solution}$:

We know, pole strength is given by,

m=$\frac{M}{l}$

A steel wire is bent into semi-circular arc, so if r is radius of semicircle, then

πr=l,

Therefore, r= $\frac{1}{\pi }$

Now new magnetic moment M′=$m\times 2r$

=$\frac{M}{l}\times \frac{2l}{\pi }$

=$\frac{2M}{\pi }$ =2M${\pi }^{-1}$

$\text{Hence B is the correct option}$