Chap5. 21

21. [P. A] Assume that in all inertial frames the force on a charged particle is given b the usual Lorentz force law: F = d p = q(E + V x B), dr where q is the charge on the particle, V = dx/dr is its three-velocity, and E and B are the electric and magnetic fields as measured in the Lorentz frame. Conside a different inertial frame moving with speed v along the x-axis with respect to the first. (a) Find the components of the four-force f in terms of E and B and the component of the particle's four-velocity u. (b) Use the transformation law for the components of f and u to find the transfer. mation rules that give the electric and magnetic fields in the new inertial fram for the following special fields in the original inertial frame: (i) An electric field in the x-direction. (ii) A magnetic field in the x-direction. (iif) An electric field in the y-direction. (iv) A magnetic field in the y-direction