The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. Find the average power per square meter carried by the EM wave. A) 720 W B) 172 W C) 500 W D) 2 × 10⁷ W E) 86 W

Question

Quizplus · Accepted Answer

The average power per square meter carried by the EM wave can be calculated using the formula:

P = (1/2) * ε0 * c * E^2

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

We first need to find the magnitude of the electric field from the given magnetic field. We can use the relationship between the magnetic field and electric field for a plane-polarized electromagnetic wave:

B = (1/c) * E

where c is the speed of light.

Rearranging this equation, we get:

E = c * B

Substituting the given value for the magnetic field, we get:

E = (3.5 x 10^-6) * (3 x 10^8) = 1050 V/m

Now we can calculate the average power per square meter:

P = (1/2) * ε0 * c * E^2

Substituting the values, we get:

P = (1/2) * (8.85 x 10^-12) * (3 x 10^8) * (1050^2) = 172 W

Therefore, the answer is B.

The Magnetic Field of a Plane-Polarized Electromagnetic Wave Moving in the Z-Direction