Question

phase between Electric and Magnetic fields in a planar Electromagnetic wave.

Can someone give a hand-waving logical explanation for the fact that the Electric and Magenetic fields of an EM wave are always in phase. ?

we know that a time varying magnetic field generates a spatially varying Electric field and vice versa. So we say that because of this they are always in phase and still keep a constant energy.

Can someone explain, how this energy propogates when both the fields reach their minima.

Answer 1

they are only in phase for a travelling wave,
in a standing wave they are 90° out of phase

Answer 2

thanks, agreed. Can you explain the scenario for a travelling wave.

Answer 3

For a plane wave along the x-axis, with \(\vec E\) along y and \(\vec B\) along z, Maxwell-Faradays equation is:

\(\LARGE\frac{\partial E(x,t)}{\partial x}\normalsize =-\LARGE\frac{\partial B(x,t)}{\partial t}\)

In the case of a travelling wave, E(x,t) = f(x-ct) and B(x,t) = g(x-ct)

Rewriting the equation above leads to:
f'(x-ct) = -(-c).g'(tx-ct) = c.g'(x-ct)

If you integrate f' and g', then f(x-ct) = c.g(x-ct)

Hence B(x,t) = E(x,t)/c

So E and B are directly proportional, whatever x, whatever t.
This implies that they must oscillate in phase.

Answer 4

thanks.