Question

A plane wave in free space has a magnetic field intensity of 0.2 A/m in the Y-direction. The wave is propagating in the Z-direction with a frequency of 3 GHz. The wavelength and amplitude of the electric field intensity are, respectively:

1. 0.05 m and 75 V/m
2. 0.10 m and 75 V/m
3. 0.05 m and 150 V/m
4. 0.10 m and 150 V/m

Answer 1

Correct Answer - Option 2 : 0.10 m and 75 V/m

Concept:

Wavelength is defined as the ratio of the speed of light in a vacuum to the frequency.

λ = c/f

λ: Wavelength

c: speed of light

f: frequency of the wave

intrinsic impedance

It is a complex quantity measured in ohms of the particular medium.

It can be shown as mentioned below:

\(\eta = \sqrt {\frac{{j\omega \mu }}{{\sigma + j\omega \in }}} = \left| \eta \right|\angle {\theta _\eta }\;\)

=|η| e^jθη

For free-space η = 120 π or 377 Ω

η = E₀/H₀

Calculation:

Given magnetic field intensity is 0.2 A/m and frequency is 3 GHz.

\(\lambda = \frac{c}{f}\)

\(\lambda = \frac{{3 \times {{10}^8}}}{{3 \times {{10}^6}}}\)

λ = 0.1 m

η = E₀/H₀

E₀ = η × H₀

E₀ = 377 × 0.2

E₀ = 75.4 V/m