Ampere's Circuital Law: Practice Problem & Solution
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.
Solution Explained:
To solve this problem, we apply the core principles of Ampere's Circuital Law. Understanding the underlying formula is key to arriving at the correct answer below:
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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