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): Conduction vs. Displacement Current.
- Conduction Current: Arises from the physical motion of charges, such as electrons, in a conductor. Occurs where free charges are present.
- Displacement Current: Defined by Maxwell, it is a time-varying electric field that induces a magnetic field, independent of charge movement. Found, for instance, in the region of a charging capacitor.
- Commonality: Both contribute to the magnetic field, as stated by the Ampere-Maxwell law: \( \oint \vec{B} \cdot d\vec{l} = \mu_0 (I_{\text{conduction}} + I_{\text{displacement}}) \).
- Distinction: Conduction current involves actual charge carriers moving, whereas displacement current is generated by a changing electric field without such movement.(b): Electromagnetic Waves in Vacuum.
Displacement current is crucial for electromagnetic wave propagation in a vacuum by ensuring the continuity of Maxwell’s equations. In a vacuum, conduction current is absent. However, a changing electric field generates a displacement current:\[I_d = \epsilon_0 \frac{d\Phi_E}{dt},\]where \( \Phi_E \) represents the electric flux. For example, an oscillating charge creates a fluctuating electric field, which in turn produces a displacement current. This displacement current then generates a magnetic field, leading to a complementary changing electric field. This self-perpetuating cycle results in the propagation of electromagnetic waves through free space.