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

[KKuff]

Homework Statement

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...

Homework Equations

E = cB
I = (E_rmsB_rms) / $\mu$₀

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.

 

[PeterO]

Homework Statement

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...

Homework Equations

E = cB
I = (E_rmsB_rms) / $\mu$₀

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.

The second formula you are using:

I = (E_rmsB_rms) / $\mu$₀

specifically refers to B_rms 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.

 

[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
B<sub>rms 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</sub>