So now we might like to consider electromagnetic waves, which are massless.
Let me give you a very simple principle of physics. The transfer of energy and the transfer of momentum go hand-in-hand. You can't have one without the other.
Now for some maths.
The force on a charged particle in an electromagnetic field is given by,
→ → → F = q(E + v × B) |
, for some charge, q , moving with velocity, v . |
We don't need to go too far from here. Clearly there is a force associated with an electromagnetic field. For a wave, the electric and magnetic fields are orthogonal to the direction of propagation. The electric field component will cause the charge to oscillate in line with the electric field. However, the magnetic field is perpendicular to the electric field, and so the induced velocity. The vector cross product gives a force in the direction of propagation. In other words, the electromagnetic wave will result in a net force in the direction of propagation. This is all we need to understand how an electromagnetic wave can transfer momentum.
This transfer of momentum is an indication that light must have momentum, as it generates a force in the direction of propagation. Given our general definition of momentum from Newton's second law, an electromagnetic wave generates a force, indicating a change in momentum. The conservation of momentum means that if light transfers momentum to a charge, it must have lost momentum to compensate.
In general, the transfer of energy must also be associated with a transfer of momentum. The mechanism for this transfer is via the combined effect of the electric and magnetic fields acting on charged particles. The key thing to note is that if you can identify that forces are involved, then by Newton's second law, momenta must be exchanged. , for some charge,
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