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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.
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 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.
Lorentz Force Law problems Problem 1 A particle with mass m and charge q is in an electric eld E and a magnetic eld B. Use Newton’s second law to write a vector di erential equation for the velocity v(t) of the particle. Write it as dv dt = Then take Cartesian components and write expressions for dv x dt = (1) dv y dt = (2) dv z dt = (3)
This case can be treated using the Lorentz force equation (5.1.1) for the force vector f acting on a charge q [Coulombs]: f = q( E + v ×μoH) [Newtons] (Lorentz force equation) (5.1.1) where E and H are the local electric and magnetic fields and v is the charge velocity vector [m s-1].
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: , v. x , x. z , z. At time t = t0 = 0, an isotropic light pulse is generated at.
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 ...
