# I Beam of Light Exerts a Force, Why?

1. Feb 9, 2016

### Sturk200

According to my optics book when you shine light on an object it exerts a pressure on the object in the direction of propagation. If light is made of alternating electric and magnetic fields, and these fields are in directions transverse to the direction of propagation, then why should the force be parallel to the direction of propagation? Shouldn't the force be in the direction that the fields are pointing?

I guess the natural explanation is that photons carry momentum... but I understand that Maxwell was one of the first to suggest a radiation pressure parallel to propagation. How would Maxwell have explained it?

2. Feb 9, 2016

### andresB

For a start the magnetic field does not produce a force in the same direction it points. But, to answer your question, in which direction points the linear momentum carried by the wave?

3. Feb 9, 2016

### marcusl

In addition you might consider, as an analogy, the Poynting vector. In which direction is energy being carried?

4. Feb 11, 2016

### drvrm

go to electromagnetic theory in any graduate text book-
The energy flux (intensity) of EM waves is expressed by the poynting vector S= EX H where E and H are field vectors;
whose magnitude we denote by S. S divided by the square of the speed of light in free space is the density of the linear momentum of the electromagnetic field.
The time-averaged intensity S divided by the speed of light is the radiation pressure exerted by an electromagnetic wave on the surface of a target, if the wave is completely absorbed:

5. Feb 12, 2016

### cpsinkule

It was known to Maxwell that the fields carry momentum. In fact, most EM books derive the radiation pressure formulas right after deriving the Field Momentum formulas. The momentum is also in the same direction as the Poynting vector.

6. Feb 13, 2016

### drvrm

The oscillations of the field vector are transverse no doubt but the propagation of the field disturbances -waves is perpendicular that is the mechanism of transverse waves found in nature- take a few day to day examples;
you drop a stone in still water the waves in water starts to expand outward - drop a piece of paper on the waves you will find the paper to oscillate vertically -the energy is transferred perpendicular to the transverse vibrations-
you can do a transverse oscillation of taught string tied at one end to a tuning fork arm- the arm vibrates perpendicular to the string but the waves generated flows along the string perpendicular to vibrations.
no doubt above examples are 'mechanical' but the EM oscillations are transverse to direction of propagation and the stress transferred in the propagation direction- the field stress which generates the energy /momentum travels in the direction of propagation.

7. Mar 3, 2016

### Sturk200

If anyone is still interested in this question, I found a good qualitative answer in Griffiths. He is talking about a plane wave traveling in the z-direction, polarized in the x-direction.

"The electric field drives charges in the x-direction, and the magnetic field then exerts on them a force (qvxB) in the z-direction. The net force on all the charges in the surface produces the pressure."

I think this was the nuts-and-bolts physical answer I was looking for.