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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.
Idea 1: Lorentz Force. charge q in an electromagnetic field experiences the force. = q(E + v × B). In particular, a stationary wire carrying current I in a magnetic field experiences the force. Z. F = I ds × B. Example 1: PPP 183. A small charged bead can slide on a circular, frictionless insulating ring.
Worksheet 2 – Lorentz Force and Biot-Savart Law 1. In a special experiment, an electron beam is passed through perpendicular electric and magnetic fields. If the electrons have a speed of 2.6 x 104 m/s, and the magnetic field is 2.5 x 10-4 T, a) what electric field strength is needed so that the electrons are undeflected?
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.
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.
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)
Example #1 –Velocity Filter Slide 14 With just the magnetic field applied, all charges experience a force in the upward direction, but that force is proportional to the velocity. Deflection appears more uniform because the inertia and velocity dependent force counteract each other. FQuB B 13 14
