Consider a point charge q at rest, situated at the origin of some frame S. Its electric field, according to S is Ē(2,1)= 1 q Ancor Of course, its magnetic field is zero. Now, you want to know what will happen to the fields if q moved to the right (positive x direction). Since it is at rest in the S frame, what you can do is go to another frame, S', then boost it to the negative x direction. This way, q moves to the right according to S'. Let the velocity of S'be v = -vi Solve for the magnetic field components as seen in the S' frame. Combine these to write down B'(.t)

Consider a point charge q at rest, situated at the origin of some frame S. Its electric field, according to S is Ē(2,1)= 1 q Ancor Of course, its magnetic field is zero. Now, you want to know what will happen to the fields if q moved to the right (positive x direction). Since it is at rest in the S frame, what you can do is go to another frame, S', then boost it to the negative x direction. This way, q moves to the right according to S'. Let the velocity of S'be v = -vi Solve for the magnetic field components as seen in the S' frame. Combine these to write down B'(.t)