Questions asked
Frank Deng
Numerade educator
The Lorentz transformations for electric and magnetic fields are given by, ar{mathbf{E}}_{|} = mathbf{E}_{|} ; ar{mathbf{E}}_{perp} = gamma(mathbf{E}_{perp} + mathbf{u} imes mathbf{B}) ar{mathbf{B}}_{|} = mathbf{B}_{|} ; ar{mathbf{B}}_{perp} = gamma(mathbf{B}_{perp} - frac{1}{c^2}mathbf{u} imes mathbf{B}) where | and perp refer to the parallel and perpendicular components with respect to the relative velocity of the reference frames. Using these transformations calculate the electric and magnetic fields of a point charge moving with a constant velocity with respect to the observer.
Mitchell Mote
PROBLEM 1 An electric charge q moves in a region of electromagnetic fields with a velocity ?u. Show that the equation of motion, dp? / d? = qu? F?? where F?? is the electromagnetic field tensor, yields the usual form of the Lorentz force.
