(Charged particles moving in magnetic fields) Magnetic field
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(Charged particles moving in magnetic fields) Magnetic fields exert forces on moving charged particles. If a particle of
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(Charged particles moving in magnetic fields) Magnetic fields exert forces on moving charged particles. If a particle of mass m and charge q is moving with velocity v in a magnetic field B, then it experiences a force F D qvB, and hence its velocity is governed by the equation m dv dt D qv B: For this exercise, suppose that the magnetic field is constant and vertical, say, B D Bk (e.g., in a cathode-ray tube). If the moving particle has initial velocity v0, then its velocity at time t is determined by 8 < : dv dt D !v k; where ! D qB m v.0/ D v0: (a) Show that v k D v0 k and jvjDjv0j for all t. (b) Let w.t / D v.t / ? .v0 k/k, so that w is perpendicular to k for all t. Show that w satisfies 8
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