Question

At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 71.9 V/m. Find the magnetic field strength B, the total energy density u, and the power flow per unit area, all at the same instant and location.

Answer 1

a) Magnetic field strength, B = 2.397 * 10⁻⁷ T

b) Total energy density, U = 4.58 * 10⁻⁸ J/m³

c) Power flow per unit area, S = 13.71 W/m²

Step-by-step explanation:

a) Electric field strength, E = 71.9 V/m

The relationship between the Electric field strength and the magnetic field strength in vacuum is:

E = Bc where c = 3.0 * 10⁸ m/s

71.9 = B * 3.0 * 10⁸

B = 71.9 / (3.0 * 10⁸)

B = 23.97 * 10⁻⁸

B = 2.397 * 10⁻⁷ T

b) Total Energy Density:

`U = (1)/(2) \epsilon_0E^2 + (1)/(2) (B^2)/(\mu_0) \\U = (1)/(2)* 8.85 * 10^(-12)*71.9^2 + (1)/(2) ((2.397*10^(-7))^2)/(4\pi*10^(-7))\\U = 2.29 * 10^(-8) + 2.29 * 10^(-8)\\U = 4.58 * 10^(-8) J/m^3`

c)Power flow per unit area

`S = (1)/(\mu_0) EB\\S = (1)/(4\pi * 10^(-7) ) * 71.9 * 2.397 * 10^(-7)\\S = 13.71 W/m^2`