PHYSICS: Have answer, but don't know how to get to it, the book doesn't have an example?

Question

The intensity of a laser beam is 450W/m^2. What is the rms value of the electric field of this laser beam? (The permittivity of free space = 8.85X10-12 C^2/Nm^2 and the permeability of free space = 4piX10-7 N/A^2.

Answer: 4.1X10^2 V/m

Please Help, thanks in advance.

Answer 1

Your book probably introduces the Poynting vector (S) which is a measure of the energy / unit area in an electromagnetic wave.

S = 1/mu0* E X B

where S, E, B are all vectors

If we use the average value of S, and the rms values of E and B, then

Savg = 1/mu0 * Erms * Brms

also the ratio of E and B is c (speed of light)

E = c * B (for either instantaneous or rms values)

so solving for E:

Erms = sqrt(mu0 * c * Savg)

If you plug in the numbers you should get 410 V/m