---
title: "9.4 GHz plane wave in dielectric"
subject: "Electromagnetism"
chapter: 4
key: "semester_3/electromagnetism:plane-wave-9-4ghz-dielectric"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/plane-wave-9-4ghz-dielectric
site: BCT Engineering
---

# 9.4 GHz plane wave in dielectric

Electromagnetism · Chapter 4: Wave equation and Wave propagation

- Asked in: 2074 Asoj, 1+1+1+2+2 marks; 2067 Shrawan, 6 marks (asked 2 times)
- Video: [UNIFORM PLANE WAVES (SOLVED PROBLEMS)](https://www.youtube.com/watch?v=JatiNpnzzQg) — Prof. Barapate's Tutorials
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/plane-wave-9-4ghz-dielectric
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-4

## Question

A 9.4 GHz uniform plane wave is propagating in a medium with ε_r = 2.25 and μ_r = 1. If the magnetic field intensity is 7 mA/m and the material is loss less, find (i) the velocity of propagation (ii) the wavelength (iii) the phase constant (iv) the intrinsic impedance (v) the magnitude of electric field intensity.

## Short answer

Using refractive index n=√(ε_r)=1.5, v=c/n=2×10⁸ m/s; λ=v/f=2.13 cm; phase constant β=2π/λ=295.3 rad/m; intrinsic impedance η=η₀/n=251.3 Ω; electric field magnitude E=ηH=1.76 V/m.

## Answer

Given: f = 9.4 GHz, ε_r = 2.25, μ_r = 1, H = 7 mA/m, lossless (σ = 0).

n = √(ε_r) = √2.25 = 1.5 (refractive index of the medium).

**(i) Velocity of propagation**

```text
v = 1/√(με) = c/√(μ_r ε_r) = 3×10⁸ / 1.5 = 2×10⁸ m/s
```

**(ii) Wavelength**

```text
λ = v/f = 2×10⁸ / 9.4×10⁹ = 0.02128 m = 2.128 cm
```

**(iii) Phase constant**

```text
β = 2π/λ = 2π / 0.02128 = 295.3 rad/m
(check: β = ω/v = 2π × 9.4×10⁹ / 2×10⁸ = 295.3)
```

**(iv) Intrinsic impedance**

```text
η = √(μ/ε) = η₀ √(μ_r/ε_r) = 120π / 1.5 = 251.3 Ω
```

**(v) Magnitude of E**

```text
E = η H = 251.3 × 7×10⁻³ = 1.759 V/m
```

**Answer:** v = 2×10⁸ m/s; λ = 2.13 cm; β = 295.3 rad/m; η = 251.3 Ω; E = 1.76 V/m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For eps_r = 2.25 and mu_r = 1, the velocity of propagation is:
   A. 3 x 10^8 m/s
   B. 2 x 10^8 m/s
   C. 4.5 x 10^8 m/s
   D. 1.33 x 10^8 m/s
   Answer: B. v = c/sqrt(mu_r eps_r) = 3 x 10^8/1.5 = 2 x 10^8 m/s. (Key point: Velocity)

2. The wavelength at 9.4 GHz is:
   A. 3.19 cm
   B. 0.64 cm
   C. 21.3 cm
   D. 2.13 cm
   Answer: D. lambda = v/f = 2 x 10^8/9.4 x 10^9 = 2.128 cm. (Key point: Wavelength)

3. The intrinsic impedance is:
   A. 377 Ω
   B. 251.3 Ω
   C. 565.5 Ω
   D. 120 Ω
   Answer: B. eta = eta0 sqrt(mu_r/eps_r) = 377/1.5 = 251.3 Ω. (Key point: Intrinsic impedance)

4. Given H = 7 mA/m, E is found as:
   A. E = H / eta = 0.028 mV/m
   B. E = eta H = 1.76 V/m
   C. E = H v = 1.4 x 10^6
   D. E = beta H = 2.07 V/m
   Answer: B. E = eta H = 251.3 x 7 x 10^-3 = 1.76 V/m. (Key point: Electric field)

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