Physics CUET UG 13-05-2025 Shift 2 Paper

Maxwell introduced the concept of displacement current $I_d$ to maintain Ampere's circuital law consistent across a charging capacitor:

• Unlike conduction current, which is produced by the physical motion of electric charges, displacement current arises solely due to a time-varying electric field (changing electric flux).
• Thus, Maxwell's displacement current is due to a changing electric field.

Standard wavelength ranges in the electromagnetic spectrum:

• X-rays: $1\,\text{nm}$ to $10^{-3}\,\text{nm}$ $\rightarrow$ (A) matches (III).
• Radio waves: $\gt 0.1\,\text{m}$ $\rightarrow$ (B) matches (IV).
• Infrared waves: $1\,\text{mm}$ to $700\,\text{nm}$ $\rightarrow$ (C) matches (I).
• Microwaves: $0.1\,\text{m}$ to $1\,\text{mm}$ $\rightarrow$ (D) matches (II).
  Correct match: (A) - (III), (B) - (IV), (C) - (I), (D) - (II).

• For an electromagnetic wave propagating in a medium with propagation constant $k$ and angular frequency $\omega$, the wave speed $c$ is given by:
  $$c = \frac{\omega}{k}$$
• From Maxwell's equations, the relationship between the peak electric field amplitude $E_0$ and peak magnetic field amplitude $B_0$ is:
  $$c = \frac{E_0}{B_0}$$
• Equating the two expressions for wave velocity:
  $$\frac{E_0}{B_0} = \frac{\omega}{k}$$