Question

The magnetic polarization results in a bound current Jb
(A) which is associated with magnetization of the material.
(B) which involves spin and orbital motion of electrons.
(C) which is the result of linear motion of charge when electric polarization changes.
(D) which is given by \( \nabla \times \vec{M} \) (where \( \vec{M} \) is magnetization).
Choose the correct answer from the options given below:

• A. (A), (B) and (C) only
• B. (A), (B) and (D) only
• C. (A), (C) and (D) only
• D. (B), (C) and (D) only

Hint:

Remember the key relationships for bound currents:
Volume bound current: \( \vec{J}_b = \nabla \times \vec{M} \)
Surface bound current: \( \vec{K}_b = \vec{M} \times \hat{n} \)
Distinguish these from electric polarization concepts:
Volume bound charge: \( \rho_b = -\nabla \cdot \vec{P} \)
Surface bound charge: \( \sigma_b = \vec{P} \cdot \hat{n} \)

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In magnetic materials, the alignment of microscopic magnetic dipoles (due to electron spin and orbital motion) creates a net macroscopic effect called magnetization (\( \vec{M} \)). This magnetization can be mathematically represented as equivalent macroscopic currents flowing within the material (bound volume current, \( \vec{J}_b \)) and on its surface (bound surface current, \( \vec{K}_b \)). These are called "bound" currents because they are due to the motion of charges bound to atoms, not free-moving charges.
Step 2: Detailed Explanation:
Let's evaluate each statement:

(A) which is associated with magnetization of the material. This is correct. Bound currents are a direct consequence of the material's magnetization \( \vec{M} \). They are a model used to describe the magnetic field produced by magnetization.

(B) which involves spin and orbital motion of electrons. This is correct. The microscopic origin of magnetization \( \vec{M} \) is the intrinsic magnetic dipole moment (spin) and orbital magnetic dipole moment of electrons in atoms. The collective alignment of these microscopic dipoles constitutes magnetization, which in turn gives rise to bound currents.

(C) which is the result of linear motion of charge when electric polarization changes. This is incorrect. The change in electric polarization \( \vec{P} \) with time gives rise to the polarization current density, \( \vec{J}_P = \frac{\partial \vec{P}}{\partial t} \). This is an electric current, not a bound magnetic current.

(D) which is given by \( \nabla \times \vec{M} \) (where \( \vec{M} \) is magnetization). This is correct. This is the definition of the bound volume current density \( \vec{J}_b \). A non-uniform magnetization (non-zero curl) within the material leads to a net flow of bound current. The bound surface current is given by \( \vec{K}_b = \vec{M} \times \hat{n} \), where \( \hat{n} \) is the normal to the surface.
Step 3: Final Answer:
Statements (A), (B), and (D) accurately describe properties and definitions related to bound magnetic currents. Statement (C) describes polarization current, which is a different concept. Therefore, the correct combination is (A), (B), and (D).