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Lecture%2018%202220%20Spring%202009

Lecture%2018%202220%20Spring%202009 - From Last Time...

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1 From Last Time Lorentz Force: F Lorentz = q ( E + v x B ) Force on wire in uniform B field: F = I L ’ x B Torque on current loop in uniform B field: t = I A x B = m x B Galvanometer Another look at the D’Arsonval galvanometer k is the tensional spring constant The angle of deflection of the pointer is directly proportional to the current in the loop The deflection also depends on the design of the meter I NAB φ κ = Charged Particle in a Magnetic Field Force on a Charged Particle Equating the magnetic and centripetal forces: Solving for r : r is proportional to the momentum of the particle and inversely proportional to the magnetic field 2 B mv F qvB r = = mv r qB = More About Motion of Charged Particle The angular speed of the particle is The angular speed, w , is also referred to as the cyclotron frequency The period of the motion is v qB ω r m = = 2 2 2 πr π πm T v ω qB = = = A charged particle is moving perpendicular to a magnetic field in a circle with a radius r . An identical particle enters the field, with v perpendicular to B , but with a higher speed v than the first particle. Compared to the radius of the circle for the first
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