Question

A magnetised wire of moment $3.14A-m^2$ is bent in the form of a semi-circle ; then the new magnetic moment will be:-

• A. $3.14A-m^2$
• B. $2A-m^2$
• C. $6.28A-m^2$
• D. $Nooneofthese$

Answer 1

The correct option is B $2A-m^2$

The pole strength of wire is assumed to be $P$ and the length is assumed $L$.

Then,

$\Rightarrow$ $P\times L=3.14A{m}^2$

The wire is then bent in the form of a semicircle.

We now, $L=3.14R$

$\Rightarrow$ The semi-circle effective length $=2R=\frac{2L}{3.14}$

$\Rightarrow$ The new magnetic moment formed in wire $=P\times \left(2R\right)$

$=\left(\frac{2L}{3.14}\right)\times P$

$=\frac{2}{3.14}\times 3.14$ [ Since, $P\times L=3.14$ ]

$=2A-m^2$