Question

The magnetic moment of a bar magnet is 0.256 amp.m${}^2$. Its pole strength is 400 milli amp. m. It is cut into two equal pieces and these two pieces are arranged at right angles to each other with their unlike poles in contact (or like poles in contact). The resultant magnetic moment of the system is

• A. $\sqrt{2}\times 256\times {10}^{-3}A{m}^2$
• B. $250\times {10}^{-3}A{m}^2$
• C. $\frac{256}{\sqrt{2}}\times {10}^{-3}A{m}^2$
• D. $\frac{128}{\sqrt{2}}\times {10}^{-3}A{m}^2$

Answer 1

The correct option is C $\frac{256}{\sqrt{2}}\times {10}^{-3}A{m}^2$

Magnetic moment of bar magnet, $M\propto l$

$M_1=\frac{M}{2}$

Therefore, $M=\frac{0.256}{2}$

resultant magnetic moment=$\sqrt{({\mu }_1{)}^2+({\mu }_1{)}^2}$

=$\frac{0.256}{\sqrt{2}}=\frac{256}{\sqrt{2}}\times {10}^{-3}$

Hence, Option c is answer.