Acquiring transverse momentum ***
In the rest frame of a particle with charge q1, another particle with charge q2 is approaching, moving with velocity v not small compared with c. If it continues to move in a straight line, it will pass a distance b from the position of the first particle. It is so massive that its displacement from the straight path during the encounter is small compared with b. Likewise, the first particle is so massive that its displacement from its initial position while the other particle is nearby is also small compared with b.
((a)) Show that the increment in momentum acquired by each particle as a result of the encounter is perpendicular to v and has magnitude q1q2/2πϵ0vb. (Gauss's law can be useful here.)
((b)) Expressed in terms of the other quantities, how large (in order of magnitude) must the masses of the particles be to justify our assumptions?