2011-05-13, 04:34 AM
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.
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.