Question

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy.

• A. I > III > II > IV
• B. I > II > III > IV
• C. I > IV > II > III
• D. III > IV > I > II

Answer 1

The correct option is C I > IV > II > III

As we know that, potential energy of a magnet in a magnetic field
$U=-m\cdot B$
$=-mB\cos \theta$
where, $m=$ magnetic dipole moment of the magnet
$B=$ magnetic field
Case I $\theta ={180}^o$
$\therefore U_1=-mB\cdot \cos {180}^o$
$=mB$ $[\because \cos {180}^o=-1]$
Case II $\theta ={90}^o$
$U_2=0$ $[\because \cos {90}^o=0]$
Case III $\theta$ is acute angle
$\theta \in (0,{90}^o)$
$\therefore \cos \theta =$ positive
Thus, $U_3=$ negative
Case IV $\theta$ is obtuse
$\theta \in ({90}^o,{180}^o)$
$\therefore \cos \theta \in (0,-1)$
Thus, $U_4=$ positive
Therefore, decreasing order of PE is
I > IV > II > III