Potential Energy of Current Loop in Magnetic Field – Rankers Physics

Force Acting on Moving Charges: Practice Problem & Solution

Assertion (A): When external magnetic field is parallel to plane of current carrying circular loop then its potential energy is maximum. Reason (R): From \(U = -MB cos\theta\) and when \(\theta = 0^{\circ}\text{ or } 180^{\circ}\), \(|cos\theta| = 1\).  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is false. If the magnetic field is parallel to the loop's plane, the magnetic dipole moment \(\vec{M}\)) is perpendicular to the field \(\vec{B}\)) (i.e., \(\theta = 90^{\circ}\)). Potential energy is \(U = -MB cos(90^{\circ}) = 0\), which is not maximum. Maximum potential energy is \(+MB\) when \(\theta = 180^{\circ}\). Reason (R) correctly states the formula for potential energy and conditions for maximum magnitude of \(cos\theta\). Given options, and (A) being false, option (4) is chosen, acknowledging (R) is factually true.

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