Magnetism question

So... from physics, when a charge is moving through a magnetic field, it experiences a force equal to F = qvB sin θ.

I understand the problems they give us about this in the textbook, but there's a conceptual thing I don't get. That equation uses the velocity of the charged particle in the field, v. But velocity isn't an absolute thing, it needs to be measured relative to something else. Relative to the ground, I might not be moving, but relative to a passing train, or the sun, I'm moving pretty fast. So what v to use?

It makes sense (based on every problem they actually give us) to use the v that assumes that the magnetic field isn't moving, but that just leads to another question, which is, how would you tell if a magnetic field is moving? Suppose it's constant and uniform, then it's still constant and uniform regardless of whether it's moving, in what direction or where, it still looks the same everywhere. But whether or not it's moving is important, because that changes what v is, which changes the magnetic force that results. Am I missing something here?

I haven't taken electromagnetism yet, so I apologize beforehand if this is unsatisfying.

The force exerted on a charge moving through a magnetic field is not just "F=q*v*B*sin(θ". The equation for the force is specifically:

F = q*v x B

Here, F, v, and B are vectors, and q is a constant. Let's say that they all have a parametrization to some quantity t:
F = (x, y, z)
v=(a(t), b(t), c(t))
B=(d(t), e(t), f(t))

The cross product here is defined as:
x = q*[b(t)*f(t)-e(t)*c(t)]
y = q*[c(t)*d(t)-f(t)*a(t)]
z = q*[a(t)*e(t)-d(t)*b(t)]

The thing here is the velocity information should be completely contained in v variable. Therefore, if for whatever reason, you decide to measure the velocity at which a uniform magnetic field moves with respect to a fixed reference point and the velocity of the charged particle with respect to the same reference point, you must subtract the values from each other to obtain the velocity of the charged particle with respect to the magnetic field. Otherwise, the parametrization of the velocity would be incompatible with the parametrization of the magnetic field, causing the equation to fail.

You must understand the situation. Where there is no explicit velocity of the field involved, velocity of the particle should be taken as the immediate relative velocity i.e. Vf = 0, and therefore you can put all the numbers in. Experimentally you have to collapse the velocity of the field (e.g. if it's a moving magnet) into the relative velocity, else you're not going to get the answer. But on paper, obviously if nothing is mentioned then assume a stationary field.

So in short, just understand the context.

Hadriel

Therefore, if for whatever reason, you decide to measure the velocity at which a uniform magnetic field moves with respect to a fixed reference point and the velocity of the charged particle with respect to the same reference point, you must subtract the values from each other to obtain the velocity of the charged particle with respect to the magnetic field.

See I kind of understand that, and if I ever got a problem like that I would do that, and none of the textbook problems are like that because the fields are assumed to be stationary. But here, I'm kind of wondering for a personal "... this doesn't quite make sense" kind of thing

Say, there's a field something like this


If the field isn't moving, then it has a value of --> (whatever that is) everywhere. If it is moving, it still has a value of --> everywhere. You can't tell the difference just by measuring the field anywhere, but it affects particles in different ways, so what is making it different?

The difference is how quickly your particle moves in relation to each of those arrows.

I want to answer seriously but it's been done and i just can't stop thinking of:

[video=youtube;OvmvxAcT_Yc]http://www.youtube.com/watch?v=OvmvxAcT_Yc&feature=related[/video]