Displacement Current: Detailed Notes for JEE Preparation

1. Definition of Displacement Current:

• Displacement current is a theoretical concept introduced by James Clerk Maxwell to provide a complete description of current flow in time-varying electric fields.
• It is a non-conducting current that arises due to the changing electric field and is related to the rate of change of electric displacement field.

Relevant NCERT References:

• NCERT Class 12 Physics, Chapter 4 (Moving Charges and Magnetism), Section 4.7 (Displacement Current)

2. Mathematical Representation:

• Displacement current density (J_D) is mathematically expressed as:

J<sub>D</sub> = ∂D/∂t

• Where:
• J_D is the displacement current density (in amperes per square meter)
• D is the electric displacement field (in coulombs per square meter)
• t is time (in seconds)

3. Relationship with Maxwell’s Equations:

• Displacement current plays a crucial role in completing Maxwell’s fourth equation, also known as the Ampere-Maxwell law.

∇⋅B = μ<sub>0</sub>(J + ∂D/∂t)

• Where:
• ∇⋅B represents the divergence of the magnetic field (B)
• μ₀ is the permeability of free space
• J is the conduction current density
• ∂D/∂t represents the displacement current density

Relevant NCERT References:

• NCERT Class 12 Physics, Chapter 4 (Moving Charges and Magnetism), Section 4.7 (Displacement Current)

4. Boundary Conditions:

• At the boundary between two different materials with permitivities ε1 and ε2, the normal component of displacement current density must be continuous:

J<sub>D1</sub>⋅n = J<sub>D2</sub>⋅n

• Where:
• J_D1 and J_D2 are the displacement current densities on either side of the boundary.
• n is the normal vector to the boundary.

Relevant NCERT References:

• NCERT Class 12 Physics, Chapter 4 (Moving Charges and Magnetism), Section 4.7 (Displacement Current)

5. Applications of Displacement Current:

• Displacement current is crucial in understanding the behavior of time-varying electromagnetic fields.
• It plays a significant role in the analysis of capacitors and inductors, and their dynamic behaviors in circuits.
• Displacement current also contributes to the propagation of electromagnetic waves, including light and radio waves, through their oscillating electric and magnetic fields.

These detailed notes provide an advanced understanding of the concept of Displacement Current, its mathematical representation, its relationship with Maxwell’s equations, boundary conditions, and its applications. Through this comprehensive understanding, engineering aspirants can enhance their preparation for the JEE examination.