(a) Characteristics of Electromagnetic Waves (1.5 Marks)

Step 1 (Foundational Principles): [0.5 Mark per point]

• Electromagnetic waves are produced by accelerated or oscillating charges.
• They do not require any material medium for propagation; they can travel through a vacuum.
• In free space, they travel with a constant speed $c$, given by the relation: $$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \approx 3 \times 10^8 \, \text{m/s}$$
• They are transverse in nature, where the oscillating electric field ($\vec{E}$) and magnetic field ($\vec{B}$) vectors are mutually perpendicular to each other and to the direction of wave propagation.

(b) Displacement Current in a Charging Capacitor (1.5 Marks)

Step 1 (Governing Law): [0.5 Mark]

The displacement current ($I_d$) arises due to the time-varying electric field between the plates of a capacitor. It is defined by the rate of change of electric flux ($\phi_E$):

$$I_d = \epsilon_0 \frac{d\phi_E}{dt}$$

Step 2 (Step-by-Step Working): [0.5 Mark]

As the capacitor charges, the charge $q$ on the plates increases with time. The electric field $E$ between the plates is given by $E = \frac{q}{A\epsilon_0}$. The electric flux through the area $A$ is:

$$\phi_E = E \cdot A = \left( \frac{q}{A\epsilon_0} \right) A = \frac{q}{\epsilon_0}$$

Substituting this into the displacement current formula:

$$I_d = \epsilon_0 \frac{d}{dt} \left( \frac{q}{\epsilon_0} \right) = \frac{dq}{dt}$$

Step 3 (Final Conclusion): [0.5 Mark]

The displacement current exists in the region between the capacitor plates where the electric field is changing. It ensures the continuity of the total current in the circuit, as $I_d$ between the plates is exactly equal to the conduction current $I_c$ flowing through the connecting wires.

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💡 EL10 Concept Insight: Think of the displacement current as a "virtual" current that bridges the gap between capacitor plates; even though no electrons physically jump across the empty space, the changing electric field acts just like a moving charge to keep the circuit's current flowing smoothly.