Displacement Current, EM Waves & Electromagnetic Spectrum - 2023 - Physics | Agrigyan

Matching electromagnetic radiation to standard frequency bands:

• X-rays have frequencies typically between $1 \times 10^{16}$ and $3 \times 10^{21}\,\text{Hz}$ (Matches I).
• Microwaves occupy frequencies from $1 \times 10^9$ to $3 \times 10^{11}\,\text{Hz}$ (Matches II).
• Radiowaves occupy the low frequency band from $5 \times 10^5$ to $10^9\,\text{Hz}$ (Matches IV).
• $\gamma$-rays have the highest frequencies, typically $1 \times 10^{18}$ to $5 \times 10^{22}\,\text{Hz}$ (Matches III).

Correct match: A-I, B-II, C-IV, D-III.

For an electromagnetic wave in vacuum, the speed of propagation $c$ is related to angular frequency $\omega$ and wave number $k$ by:

The ratio of the electric field amplitude $E_0$ to the magnetic field amplitude $B_0$ is also equal to the speed of light $c$:

Cross-multiplying:

Displacement current is that current which arises due to the time rate of change of electric flux (time-varying electric field) between the plates of a charging capacitor or in free space.
According to Maxwell's formulation:

where $\Phi_E = \int \vec{E} \cdot d\vec{A}$ is the electric flux and $\varepsilon_0$ is the permittivity of free space.