Chapter 21, Problem 19 An ?-particle has a charge of +2 e and a mass of 6.64 10

Question

Chapter 21, Problem 19

An ?-particle has a charge of +2e and a mass of 6.64 10-27 kg. It is accelerated from rest through a potential difference that has a value of 1.68 106 V and then enters a uniform magnetic field whose magnitude is 1.96 T. The ?-particle moves perpendicular to the magnetic field at all times. What is (a) the speed of the ?-particle, (b) the magnitude of the magnetic force on it, and (c) the radius of its circular path?

An ?-particle has a charge of +2e and a mass of 6.64 10^-27 kg. It is accelerated from rest through a potential difference that has a value of 1.68 10^6 V and then enters a uniform magnetic field whose magnitude is 1.96 T. The ?-particle moves perpendicular to the magnetic field at all times. What is (a) the speed of the ?-particle, (b) the magnitude of the magnetic force on it, and (c) the radius of its circular path? > Chapter 21, Problem 19

Explanation / Answer

q = +2e, m = 6.64*10-27 kg. V =1.68*106 V, B =1.96 T.

(a) What is the speed of the?-particle?
2qV = mv2/2
?v = ?(4qV/m) = 1.272*107 m/s

(b) What is the magnitude of the magnetic force on it?
F = 2*qvB = 7.98*10-12 N

(c) What is the radius of its circular path?
F = mv2/r
?r = mv2/F = 0.1346 m

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