The magnetic field of an electromagnetic wave has a peak value of 5.0 × 10^-10 T.What is the intensity of the wave? (c = 3.0 × 10⁸ m/s,c = 3.00 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A, A) 1.0 × 10^-13 W/m² B) 1.5 × 10^-5 W/m² C) 3.0 × 10^-5 W/m² D) 2.0 × 10^-13 W/m² E) 7.5 × 10⁵ W/m²

Question

Quizplus · Accepted Answer

The intensity (I) of an electromagnetic wave is given by:

I = (cε0/2)E^2

where c is the speed of light, ε0 is the permittivity of free space, and E is the peak value of the electric field.

We are given the peak value of the magnetic field, Bpeak = 5.0 × 10^-10 T. The relationship between the peak value of the electric field (Epeak) and the peak value of the magnetic field (Bpeak) is given by:

Epeak = cBpeak

Substituting in the given values, we have:

Epeak = (3.0 × 10^8 m/s)(5.0 × 10^-10 T) = 1.5 × 10^-1 V/m

The intensity of the wave is then:

I = (cε0/2)Epeak^2 = (3.0 × 10^8 m/s)(8.85 × 10^-12 F/m)(1.5 × 10^-1 V/m)^2/2 = 3.0 × 10^-5 W/m^2

Therefore, the best choice is C.

The Magnetic Field of an Electromagnetic Wave Has a Peak