sol66
Mar19-11, 08:58 PM
1. The problem statement, all variables and given/known data
Assume that in all inertial frmaes the force on a charged particle is gen in the usual Lorentz force law:
F = dp/dt = q(E + V x B) **(p is the relativistic 3 vector momentum)
Components of the four-force needs to be expressed in terms of E and B.
2. Relevant equations
F = (\gamma*F*V, \gamma*q(E + V x B) "3 vector portion")
4 Vector Momentum = P = m\gamma, m\gammav "3 vector portion")
3. The attempt at a solution
So when attempting to solve this problem, I took the derivative of the relativistic 3 momentum vector and got ...
(dv/dt)(m\gamma + \gamma^3v^2] = q(E + V x B)
My problem is that after look at this equation, I've realized that it is too difficult to solve for v in terms of E and B ... so there must be something I'm doing wrong. If I could solve for v then I could just simply plug it in my four vector formulas for force and velocity. I need to find the components for those vectors. Any idea how to fix this? Thanks.
Assume that in all inertial frmaes the force on a charged particle is gen in the usual Lorentz force law:
F = dp/dt = q(E + V x B) **(p is the relativistic 3 vector momentum)
Components of the four-force needs to be expressed in terms of E and B.
2. Relevant equations
F = (\gamma*F*V, \gamma*q(E + V x B) "3 vector portion")
4 Vector Momentum = P = m\gamma, m\gammav "3 vector portion")
3. The attempt at a solution
So when attempting to solve this problem, I took the derivative of the relativistic 3 momentum vector and got ...
(dv/dt)(m\gamma + \gamma^3v^2] = q(E + V x B)
My problem is that after look at this equation, I've realized that it is too difficult to solve for v in terms of E and B ... so there must be something I'm doing wrong. If I could solve for v then I could just simply plug it in my four vector formulas for force and velocity. I need to find the components for those vectors. Any idea how to fix this? Thanks.