# Expansion of Electromagnetic waves

1. May 19, 2004

### Feynmanfan

Hi there Physics masters!

How on earth do electromagnetic waves expand at the speed of light to infinity (in vacuum) if we've learned that the electric and magnetic fields vary inversely proportional to the square of the distance?

I don't know if it's a stupid question but I'm quite baffled about it.

Thanks!

2. May 19, 2004

### Integral

Staff Emeritus
I do not understand what your problem is? Could you please elaborate?

3. May 19, 2004

### Feynmanfan

Certainly.

Well, as in my first electromagnetism course I've learned that the electric field and magnetic field are both inversely propotional to the square of the distance.

Now, electromagnetic waves can expand infinetely in space and can carry ENERGy (that's what I felt today at the beach, the sun was burning!). SO my question is, how is it that these waves can carry energy and can expand to infinity in vacuum if the fields that create them vary inversely proportional to the square of the distance.

I'm a first year physics student so if you think this question has no sense just tell me and I'll think about something else.

4. May 19, 2004

### robphy

Electrostatic fields of a point charge are inverse-square.
This is one configuration of the electromagnetic field.

A plane electromagnetic wave is a different configuration of the electromagnetic field.
This configuration involves a dynamical electric field and a dynamical magnetic field, which sustain each other and propagate disturbances at the speed of light.

5. May 19, 2004

### Staff: Mentor

I'm a little puzzled that you are puzzled!

It is certainly possible for EM waves to be emitted from a "point" source and expand outward, carrying energy. Since the wave covers the entire area of an expanding sphere, wouldn't you think that its energy is also spread out in an inverse square pattern?

Note that it's the energy per unit area that drops off according to an inverse square law, not the field itself. The energy per unit area carried by the field is reflected by the size of the field squared--so the amplitude of the field actually drops off linearly. Does that make some sense?

Last edited: May 19, 2004
6. May 20, 2004

### Feynmanfan

Thanks.

Now I understand