# Intensity of an electromagnetic wave, given only rms value of magnetic field

1. Jul 30, 2011

### KKuff

1. The problem statement, all variables and given/known data
Hi, here is the problem I'm having trouble with:

The rms value of the magnitude of the magnetic field in an electromagnetic wave is Brms = 0.137 T. The intensity of this wave is approximately...

2. Relevant equations

E = cB
I = (ErmsBrms) / $\mu$0

3. The attempt at a solution

E = (3 x 108)(0.137 T) = 4.11 x 107 V/m
I = ((4.11 x 107 V/m)(0.137 T)) / (4$\pi$ x 10-7) = 4.47 x 1012 W/m2

I keep re-doing this problem and I keep coming up with that same answer, but it is not one of the answer choices. Can anyone give me a clue as to what I'm doing wrong? Thanks, I appreciate it.

2. Jul 30, 2011

### PeterO

The second formula you are using:

I = (ErmsBrms) / $\mu$0

specifically refers to Brms while the first

E = cB

Just refers to B.

Does that mean you should change the RMS value into some other type of value before substituting?

Not claiming that is correct, just a thought.

3. Jul 30, 2011

### KKuff

Thanks for the reply.
I believe that that formula works both for rms values and peak values.

This should give me the rms value of the electric field
E = (3 x 108)(0.137 T) = 4.11 x 107 V/m

If I convert the magnetic field rms value to peak I would get
Brms x $\sqrt{}2$ = Bpeak
0.137 T x $\sqrt{}2$ = 0.194 T

and using E = cB
Epeak = 5.82 x 107

and converting to rms
(5.82 x 107) / $\sqrt{}2$ = 4.11 x 107 V/m