Field intensity: 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, ε₀ = 8.85 × 10^-12 C²/N ∙ m²) 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 of an electromagnetic wave is given by the formula:
$I = \frac{1}{2} \epsilon_0 c E_{max}^2$
Where $\epsilon_0$ is the electric constant, $c$ is the speed of light, and $E_{max}$ is the peak electric field amplitude.

We are given the peak value of the magnetic field $B_{max}$, and we know that $B_{max}=cE_{max}/\mu_0$, where $\mu_0$ is the magnetic constant. Therefore, we can solve for $E_{max}$:
$E_{max}=B_{max}\mu_0/c$

Substituting this expression into the formula for intensity, we get:
$I = \frac{1}{2} \epsilon_0 c (B_{max}\mu_0/c)^2 = \frac{1}{2} \epsilon_0 \mu_0 B_{max}^2$

Plugging in the given values, we get:
$I = \frac{1}{2} (8.85 	imes 10^{-12} C^2/Nm^2) (4\pi 	imes 10^{-7} Tm/A)^2 (5.0 	imes 10^{-9} T)^2 = 2.99 	imes 10^{-5} W/m^2$

Therefore, the best choice is C.

Field Intensity: the Magnetic Field of an Electromagnetic Wave Has