# Find Magnetic Field Amplitude from EM Wave Amplitude

1. May 1, 2013

### tquiva

1. The problem statement, all variables and given/known data

A plane electromagnetic wave propagating in free space has an amplitude ($\sqrt{3}$/2)a$_{y}$-(1/2)a$_{z}$ V/m. Find the amplitude of the accompanying magnetic field assuiming the frequency of the electric field is 1 GHz.

2. Relevant equations

f$_{E}$ = f$_{H}$

$\frac{E_{0}}{B_{0}}$ = $\frac{ω}{k}$ = c

3. The attempt at a solution

I know that the frequency for both the Electric and Magnetic fields are equivalent. Therefore, the magnetic field frequency is also 1 GHz.

However, the question says "electromagnetic wave." This term means the cross product result or E x B right? With that being said, I'm not sure how to obtain the amplitude of the magnetic field if I don't have any info for the electric field.

Or is there some other equation related to the EM wave?

Any help or suggestions is greatly appreciated!

2. May 1, 2013

### Simon Bridge

But you are provided with "info for the electric field": the frequency and the amplitude. What else do you need?

For EM radiation the E and B components have a special relationship.

3. May 2, 2013

### ehild

Perhaps it was meant the vector amplitude of the electric field.

ehild