Question

Two identical thin bar magnets each of length $l$ and pole strength $m$ are placed at right angle to each other with north pole of one touching south pole of the other. Magnetic moment of the system is

• A. $ml$
• B. $2ml$
• C. $\sqrt{2}ml$
• D. $ml/2$

Answer 1

The correct option is C $\sqrt{2}ml$

Given that,

Length of bar magnet = $L$

Pole strength = $m$

Let the pole strength of the system magnets be $m$ and length $N_2{S}_1$

But,

$N_2{S}_1=\sqrt{{\left(N_1{S}_1\right)}^2+{\left(N_2{S}_2\right)}^2}$

$N_1{S}_1=N_2{S}_2=L$

$N_2{S}_1=\sqrt{L^2+L^2}$

$N_2{S}_1=L\sqrt{2}$

Magnetic moment of the system

$M=m\times N_2{S}_1$

$M=m\times L\sqrt{2}$

$M=mL\sqrt{2}$

Hence, the Magnetic moment of the system is $mL\sqrt{2}$