Question

A short bar magnet placed with its axis at ${30}^o$ with a uniform external magnetic field of $0.16T$ experiences a torque of magnitude $0.032Nm$ If the bar magnet is free to rotate, its potential energies when it is in stable and unstable equilibrium are respectively

• A. $-0.064J,+0.064J$
• B. $-0.032J,+0.032J$
• C. $+0.064J,-0.128J$
• D. $0.032J,-0.032J$
  

Answer 1

The correct option is A $-0.064J,+0.064J$

$\theta ={30}^o$
$B=0016T$
$z=0.032$
$z=mB\sin \theta$
$0.032=m\times \frac{1}{2}\times 0.16$
$m=0.4Am$
$U=-\overrightarrow{m}.\overrightarrow{B}$
$U_{max}=mB=0.4\times 0.16=0.064T$
$U_{min}=-mB=-0.4\times 0.16=-0.064T$