How do waves have momentum? - by Mark John Fernee - Quora Question review

This document contains a review of the answer by Mark John Fernee on the question in Quora: "How do waves have momentum? "
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Reflection

1. Answer Review by Mark John Fernee

Let's start with the basics. A force is defined by the rate of change in momentum.
Let's start with the basics: What means rate of change in momentum.
This is just Newton's second law in a more general form.
Let's start with the basics: What is Newton's second law.
That means that if a wave generates a force, then it must have momentum.
Let's start with the basics: What is meant with a wave?
I'm guessing that anyone who's been to the beach will have experienced the force of a wave. Similarly with acoustic waves, which cause things to vibrate. You may have experienced a supersonic shock wave, which can shake your house and even break windows.
All of that, I expect, most people understand. If you start with these examples, explaining waves, maybe, the whole answer becomes easier to understand.

So now we might like to consider electromagnetic waves, which are massless.

Again lets go back to the basics: What means mass and what means massless? A different issue is: how is mass measured or calculated?
However, don't let that massless property fool you. Have you ever warmed yourself in the sun? Clearly we have no problem with electromagnetic waves delivering heat. Heat is a form of energy. We ultimately get all our energy from the sun. That energy is delivered by light.
But here something is not clear. Why does light, which is also a wave, has no mass

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.

There is a more basic problem: Energy and momentum are mathematical concepts related to the same physical phenomena.
What we need to do is associate energy with force. This is where the concept of potential energy is important. A force can be expressed as the gradient of some potential energy. Therefore, we have a force represented by the gradient of a potential, as well as the rate of change of momentum. Forces are the glue that bind energy and momentum as two different aspects of the same phenomenon.

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,

Reflection 1 - Question Review: How do waves have momentum?

To try to understand you should only use experiments.
1) Search for a straight way which goes from the top of one hill to an other hill. Place a car op the top of the hill. Push slightly against the car. The car will start to roll downwards. First slowly and then faster and faster. When the car reaches the bottom its spead will be the highest, then the car will start to roll upwards and the spead will decrease, untill the car stops.
A different way to describe this is that original when the car is at the top of the hill the momentum of the car is zero. When the spead increases the momentum increases. When the car is at the bottom of the hill, the momentum is the highest. There after the momentum decreases untill the car stops. At that moment the momentum is again zero.
2) Next perform a slightly different experiment. This starts the same as the first but when the spead increases try to stop the car. That means you place in front of the car and when it reaches you, you must push against the car untill it stops. 3) Next place some stones in the car in the car and repeat the same experiment. What you will experience that it is much more difficult to stop the car. This comes because the mass of the car has increased and also the momentum.

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Created: 26 May 2024

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