Question

(a) Differentiate between 'conduction current' and 'displacement current', giving one similarity and one dissimilarity between them.
(b) Explain the existence of electromagnetic waves in free space, using the concept of displacement current.

Hint:

For electromagnetic wave problems: - Displacement current \( I_d = \epsilon_0 \frac{d\Phi_E}{dt} \) bridges the gap in Maxwell’s equations in free space. - It ensures that changing electric and magnetic fields sustain each other, enabling wave propagation.

Answer 1

(a): Differentiate between conduction and displacement current.
- Conduction Current: This is the current due to the actual movement of charges (e.g., electrons) in a conductor, such as in a wire. It occurs in materials with free charges.
- Displacement Current: Introduced by Maxwell, this is a time-varying electric field that produces a magnetic field, even without charge movement. It exists in regions like the gap of a charging capacitor.
- Similarity: Both contribute to the magnetic field, as per the Ampere-Maxwell law: \( \oint \vec{B} \cdot d\vec{l} = \mu_0 (I_{\text{conduction}} + I_{\text{displacement}}) \).
- Dissimilarity: Conduction current involves the physical movement of charges, while displacement current arises from a changing electric field without charge movement. (b): Electromagnetic waves in free space.
Displacement current enables electromagnetic waves in free space by ensuring continuity in Maxwell’s equations. In a vacuum, there is no conduction current, but a changing electric field creates a displacement current: \[ I_d = \epsilon_0 \frac{d\Phi_E}{dt}, \] where \( \Phi_E \) is the electric flux. For example, an oscillating charge produces a varying electric field, leading to a displacement current. This displacement current generates a magnetic field, which in turn induces a changing electric field. This self-sustaining process results in the propagation of electromagnetic waves in free space.