Question

A current carrying loop of radius $2cm$ has $4A$ current flowing in an anti-clockwise direction. The plane of the loop makes an angle of $\theta$ with the direction of the magnetic field which is in an upward direction. the value of the magnetic field is $0.7Tesla$.if potential energy of loop in magnetic field is $\approx 0.01J$, then value of $\theta$ is:

• A. ${45}^0$
• B. ${60}^0$
• C. ${30}^0$
• D. None of these

Answer 1

The correct option is C ${30}^0$

Potential energy $=\mu B=\mu B\cos \theta$ where $\mu =$magnetic moment

$\mu =iA$ where $A$= Area of loop

$p_E=iA\cos \theta \times B=0.01$

$0.7\times 4\times \pi \times 4\times {10}^{-4}\cos \theta =0.01$

$\cos \theta =\frac{0.01\times {10}^{-4}}{16\pi \times 0.7}=\frac{100}{50\times 0.7}=\frac{2}{0.7}$

$\cos \theta >1$ is not possible.

So option C is correct.