Find electric and magnetic field amplitudes in an electromagnetic wave

[Cade]

[Solved] Find electric and magnetic field amplitudes in an electromagnetic wave

Homework Statement

Find the electric and magnetic field amplitudes in an electromagnetic wave that has an average energy density of 1 J/m^3

Homework Equations

u = Energy density
u = (1/2)(e0)(E^2) + (1/2)(B^2/u0)
or u = (e0)(E^2)
or u = (B^2)/u0

E = cB, c = speed of light

The Attempt at a Solution

Let's find E first:
u = e0*E^2
E = sqrt(u/e0) = sqrt(1/(8.85*10^-12)) = 336146 V/m
336146 V/m is apparently wrong for E. Let's try B instead

u = (B^2)/u0
B = sqrt(u*u0) = 0.001121 T
Now let's try E = cB to find E
E = (3*10^8)(0.001121) = 336300 V/m

But both E and B are wrong. What am I missing? Percent error tolerance for a correct answer is 10%.

 

[SammyS]

I think your answers are for the RMS values of the fields, rather than for the peak values. The peak values are generally used for the amplitude of a wave.

Try multiplying your answers by √(2) .

 

[Cade]

Edit: This is the equation I used, I have Uav = 1 J/m^3

Edit: Oh, I see. Thanks. :)