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If we have both electric and magnetic fields, the total force that acts on a charge is of course given by F~ = q E~ + ~v c ×B~!. This combined force law is known as the Lorentz force. 10.1.1 Units The magnetic force law we’ve given is of course in cgs units, in keeping with Purcell’s system.
Derivation of Lorentz Force Law. We begin with the assumption that a particle with rest mass m, charge q and no velocity moves according to Newton’s law (because it is at or nearly at rest) with a force given by the electric field.
Electromagnetism IV: Lorentz Force. The problems here mostly use material covered in previous problem sets, though chapter 5 of Purcell covers relativistic field transformations. For further interesting physical examples, see chapter II-29 of the Feynman lectures. There is a total of 81 points.
Derivation of Lorentz Transformations. Consider two coordinate systems (x; y; z; t) and (x0; y0; z0; t0) that coincide at t = t0 = 0. The unprimed system is stationary and the primed system moves to the right along the x¡direction with speed v: The Galilean transformation does not work.
We begin with a space-time diagram, Fig. 1, which shows the coordinate axes txyz of a Lorentz frame as well as a light cone. The light cone has the equation, c2t2 = x2 + y2 + z2. (1) It consists of two parts, the forward and backward light cones, the parts t > 0 and t < 0, respectively.
7.1.1 Lorentz Transformations in Three Spatial Dimensions In the above derivation, we ignored the transformation of the coordinates y and z perpendicular to the relative motion. In fact, these transformations are trivial. Using the above arguments for linearity and the fact that the origins coincide at t =0,the most general form of the ...
Input Skills: Solve problems involving relative motion using the Galilean trans-formation (MISN-0-11). State the postulates of special relativity (MISN-0-73).
