Three different particles enter a region of magnetic field as shown at the right

Question

Three different particles enter a region of magnetic field as shown at the right. All particles have the same speed, v- 0.3x10 m/s and all particles have the same charge lg 80x10", C. The magnetic field has magnitude lBl = 0.9 T and d = 2.0 cm. I. . .B The magretic dall a) 15 pts] Are the particles positively or negatively charged? Explain Detector b) [5 pts] Find the mass of the particle that reaches the detector. Hin,2F mac = m. c) 15 pts] Does the particle that follows the rightmost trajectory have more, less, or the same mass as the one that reaches the detector? Explain Extra Credit [5 pts] If the particle that reaches the detector were traveling freely in this magnetic field, what would be the "cyclotron frequency" associated with its motion?

Explanation / Answer

a)By flemings right hand rule, the motion of the particles indicate that they are negatively charged.

b)radius of trajectory = 0.5*d

so, balancing the centrifugal and mabnetic forces,

mv^2/r = qv*B

or m= 8*10^-19*0.9*0.01/(0.3*10^6)

or m=2.4*10^-26 kg

c)as mass increases, the radius increases. hence it has more mass.

Extra credit:

w = qB/m

=8*10^-19*0.9/(2.4*10^-26)

=3*10^7 rad/s

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