Using Maxwell's equations it can be shown that electromagnetic waves have a speed in free space of A)(ε_Oμ_O)^-3/2. B)(ε_Oμ_O)^-1/2. C)ε_Oμ_O. D)(ε_Oμ_O)^-2. E)(ε_Oμ_O)^-1.

Question

Quizplus · Accepted Answer

Maxwell's equations in free space are:$$
abla \cdot E = 0$$$$
abla \cdot B = 0$$$$
abla 	imes E = -\frac{\partial B}{\partial t}$$$$
abla 	imes B = \mu_0 \epsilon_0 \frac{\partial E}{\partial t}$$Taking the curl of the third equation and using the fourth equation, we get:$$
abla 	imes (
abla 	imes E) = -\mu_0 \epsilon_0 \frac{\partial^2 E}{\partial t^2}$$Using the vector identity:$$
abla 	imes (
abla 	imes A) = 
abla (
abla \cdot A) - 
abla^2 A$$we get:$$
abla^2 E - \mu_0 \epsilon_0 \frac{\partial^2 E}{\partial t^2} = 0$$This is the wave equation for the electric field. The speed of the wave is given by:$$v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$$Therefore, the correct answer is B.

Using Maxwell's Equations It Can Be Shown That Electromagnetic Waves