## anonymous one year ago Relationship between electric field and magnetic field?

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1. Michele_Laino

Hint: you have to consider the relationship between the electric field and magnetic field of a plane electromagnetic wave.

2. IrishBoy123

delve into the Maxwell/ Heaviside equations....

3. IrishBoy123

you will be amazed

4. anonymous

Could you explain me @Michele_Laino

5. Michele_Laino

the electric and magnetic field of a plane electromagnetic wave can be represented as below: |dw:1438869598405:dw|

6. Michele_Laino

the magnetic and electric field can be represented by these vectors: $\Large \begin{gathered} {\mathbf{E}} = {{\mathbf{E}}_0}{e^{i\left( {{\mathbf{k}} \cdot {\mathbf{r}} - \omega t} \right)}} \hfill \\ \hfill \\ {\mathbf{B}} = {{\mathbf{B}}_0}{e^{i\left( {{\mathbf{k}} \cdot {\mathbf{r}} - \omega t} \right)}} \hfill \\ \end{gathered}$ using the Maxwell equation, we can show this: $\Large {\mathbf{E}} = \frac{{{\mathbf{k}} \times {\mathbf{B}}}}{\omega }$ being $\Large {\mathbf{k}}$ the wave vector, whose modulus, is: $\Large \left| {\mathbf{k}} \right| = \frac{\omega }{c}$