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# lecture19 - Charged Particles in Electric and Magnetic...

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Charged Particles in Electric Charged Particles in Electric and and Magnetic Fields Magnetic Fields Motion of charged particles Lorentz Force Examples: cyclotron, mass spectrometer

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Recall: Recall: in general, “Lorentz Force” E q F = E q B v q F + × = in a magnetic field B v q F × = in an electric field
Magnetic Fields: Magnetic Fields: F F = = q q v v × × B B q x x x x x x x x v v F F + Theforce is perpendicular to the velocity (and path), so: no work is doneby B kinetic energy is constant speed is constant Only the direction of the motion changes dueto the magnetic force. B B

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1) Uniform 1) Uniform B B , , v v perpendicular to perpendicular to B B + q v x x x x x x x x Motion is a circle . F Magnetic force ( v ) is F m = qvB (constant) But F c = mv 2 /r , so the radius of circle is : mv r qB = r
Example: Example: A proton is moving in a circular orbit of radius 14cm in a uniform magnetic field of 0.35T directed perpendicular to the velocity of the proton. Find theorbital speed of the proton.

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