# lecture20 - Magnetic Fields(III Text sections 29.4 29.6...

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Magnetic Fields (III) Text sections 29.4 – 29.6 •Motion of charged particles in magnetic fields •Examples: cyclotron, mass spectrometer, Hall effect For practice: Chapter 29, problems 29, 33, 45, 47, 49 Charged Particles in Electric and Magnetic Fields Charged Particles in Electric and Magnetic Fields or in general, (“Lorentz Force”) B v q F r r r × = E q B v q F r r r r + × = in a magnetic field

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Magnetic Fields: Magnetic Fields: F = q v × B q xxx xx v F + The force is perpendicular to the motion, so: no work is done kinetic energy is constant speed is constant Only the direction of the motion changes due to the magnetic force. B 1) Uniform 1) Uniform B , , v perpendicular to perpendicular to B + v r Motion is a circle . F r Radial acceleration ( v ) is a r = F/m = qvB/m (constant) But a r = v 2 /r , so the radius of curvature r is constant.
Start with Newton’s 2 nd Law: a m F r r = r v m B v q 2 = From this, calculate radius, speed, etc… , qvB F = r r v a 2 = Then replace: (Newton’s 2 nd Law for a particle in a uniform

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lecture20 - Magnetic Fields(III Text sections 29.4 29.6...

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