MHT CET · Physics · Magnetic Effects of Current
A magnetic dipole of magnetic moment \(\mathrm{M}\), is freely suspended in a magnetic field of induction \(B\). The minimum and maximum value of potential energy of the dipole, respectively are
- A \(-\mathrm{MB},+\mathrm{MB}\)
- B \(0, \mathrm{MB}\)
- C \(0,2 \mathrm{MB}\)
- D \(\mathrm{MB}, 0\)
Answer & Solution
Correct Answer
(A) \(-\mathrm{MB},+\mathrm{MB}\)
Step-by-step Solution
Detailed explanation
The potential energy of the magnetic dipole is given by \(\mathrm{U}=-\mathrm{MB} \cos \theta\)
Where \(\theta\) is the angle between \(\vec{M}\) and \(\vec{B}\)
For \(\theta=0^{\circ}, \mathrm{U}=-\mathrm{MB} \cos \theta^{\circ}=-\mathrm{MB}\) (Minimum)
For \(\theta=180^{\circ}, \mathrm{U}=-\mathrm{MB} \cos 180^{\circ}=\mathrm{MB}\) (Maximum)
Where \(\theta\) is the angle between \(\vec{M}\) and \(\vec{B}\)
For \(\theta=0^{\circ}, \mathrm{U}=-\mathrm{MB} \cos \theta^{\circ}=-\mathrm{MB}\) (Minimum)
For \(\theta=180^{\circ}, \mathrm{U}=-\mathrm{MB} \cos 180^{\circ}=\mathrm{MB}\) (Maximum)
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