Question

Identify the wrong statement

• A. Current loop is equivalent to a magnetic dipole
• B. Magnetic dipole moment of a planar loop of area \(A\) carrying current \(I\) is \(I^2A\)
• C. Particles like proton, electron carry an intrinsic magnetic moment
• D. The current loop placed in uniform magnetic field experiences torque \(\vec{\tau} = \vec{m} \times \vec{B}\)
• E. Ampere’s circuital law is not independent of Biot Savart’s law

Hint:

Always remember \(m = IA\), not \(I^2A\).

Answer 1

The Correct Option is B

Concept: Magnetic dipole moment of a current loop is defined as: \[ \vec{m} = I \vec{A} \] It depends linearly on current and area.

Step 1: Check option (A).
A current loop produces a magnetic field similar to a bar magnet → correct.

Step 2: Check option (B).
Given: \(I^2A\), but correct formula is: \[ m = IA \] Thus this is incorrect.

Step 3: Check option (C).
Electrons and protons possess intrinsic spin → magnetic moment → correct.

Step 4: Check option (D).
Torque on dipole: \[ \vec{\tau} = \vec{m} \times \vec{B} \] Correct.

Step 5: Check option (E).
Ampere’s law can be derived from Biot–Savart law → not independent → correct.

Step 6: Conclusion. \[ \boxed{(B)} \]