Chapter 27: Charged particles Chapter outline ■
determine the size and the direction of the force on a charge moving in a magnetic field
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derive the expression VH =
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describe and analyse the deflection of beams of charged particles by uniform electric and uniform magnetic fields explain how electric and magnetic fields can be used in velocity selection e explain the main principles of one method for the determination of v and me for electrons
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BI ntq
for the Hall voltage, where t = thickness
KEY TERMS
Fleming’s left-hand rule: if the first finger of the left hand is pointed in the direction of the magnetic field and the second finger in the direction of the conventional current, then the thumb points in the direction of the force or motion produced Equations: F = BQv sinθ F = qE E= V d
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2 acceleration in a circle a = v = ω 2r r v = rω
F = ma VH =
BI ntq
I = Anvq
Exercise 27.1 Magnetic forces on particles In this exercise, you need to equate the formula for the magnetic force to the centripetal force. You also need to understand the various directions of fields and movement for particles of positive and negative charge. charge on an electron = −1.6 × 10−19 C mass of an electron = 9.1 × 10−31 kg mass of a proton = 1.7 × 10−27 kg 1 Look at this formula for the force F acting on a charged particle in a magnetic field of flux density B: F= BQv sinθ a State the meaning of the symbols Q, v and θ. b Describe what a charged particle must do to experience a force in a magnetic field. c State two situations in which there is no magnetic force on a charged particle, even though it is in a magnetic field.