Current Loop in Magnetic Field – Rankers Physics
Topic: Magnetic Effects of Current
Subtopic: Ampere's Circuital Law

Current Loop in Magnetic Field

Assertion (A): A rectangular current loop is in an arbitrary orientation in an external uniform magnetic field. No work is required to rotate the loop about an axis perpendicular to its plane.
Reason (R): All positions represent the same level of energy.
 
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

Solution:

Assertion (A): A current loop in a uniform magnetic field experiences a torque \(\vec{\tau} = \vec{M} \times \vec{B}\). Work is generally required to change its orientation. So, (A) is false. Reason (R): The potential energy of a current loop in a magnetic field is \(U = -\vec{M} \cdot \vec{B}\), which depends on the orientation of \(\vec{M}\) relative to \(\vec{B}\). Thus, not all positions represent the same energy. So, (R) is false. Both (A) and (R) are false.

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