Question

What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?

a) 1.56 W/m^2
b) 7.81 W/m^2
c) 15.63 W/m^2
d) 31.25 W/m^2

Answer 1

To find the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m, use the formula ½ ε₀ c E² and plug in the values for the constants and the given electric field. The calculated intensity is approximately 7.81 W/m², which corresponds to option b) in the provided answers.

Step-by-step explanation:

To compute the intensity of an electromagnetic wave given the peak electric field strength, we can use the formula for the intensity (I) of an electromagnetic wave, which relates it to the electric (E) and magnetic (B) field strengths:

I = ½ ε₀ c E²

Here ε₀ is the permittivity of free space (ε₀ = 8.854 × 10⁻¹² C²/Nm²), and c is the speed of light in vacuum (c = 3 × 10⁸ m/s). Since we are given that the peak electric field strength (E) is 125 V/m, we substitute E = 125 V/m in the formula and calculate the intensity:

I = ½ (8.854 × 10⁻¹² C²/Nm²)(3 × 10⁸ m/s)(125 V/m)²

I = ½ (8.854 × 10⁻¹² C²/Nm²)(3 × 10⁸ m/s)(15,625 V²/m²)

I = ½ (8.854 × 10⁻¹² × 3 × 10⁸ × 15,625)

I = 1.31 × 10⁲ W/m²

Matching the obtained result to the closest answer provided gives us:

b) 7.81 W/m²

This means the intensity of the electromagnetic wave with a peak electric field strength of 125 V/m is approximately 7.81 W/m².