A beam of particles (each particle has a charge q = -2e and a kinetic energy of

Question

A beam of particles (each particle has a charge q = -2e and a kinetic energy of 4.00 x 10^-13 J) is deflected by the magnetic field of a bending magnet as shown in Figure 19-32. The radius of curvature of the beam ?s 20.0 cm, and the strength of the magnetic field ?s 1.50 T. (a) What is the mass of the par- tides making up the beam? (b) Sketch the path for the given ions in the given magnetic field as a reference path. Then sketch a path for a more massive doubly ionized negative ion and a less massive doubly ionized positive ion, both with the same speed as the given ions, for comparison. Answer: (a) 1.15 x 10^-26 kg

Explanation / Answer

The magnetic force acting on the beam particle provides the necessary centripetal acceleration to move in circle

Fmagnetic = Fcentripetal

q V B = m V2 /r

m V2 = q V B r

dividing both side by 2

m V2/2 = q V B r/2

KE = q V B r/2                      ( since KE = m V2/2 =4 x 10-13 )

4 x 10-13 = (1.6 x 10-19 C) V (1.5 T) (0.2 m) /2      (Since q = 1.6 x 10-19 C , B = 1.5 T , r = 20 cm = 0.2 m)

V = 8.33 x 106 m/s

Since    KE = m V2/2 =4 x 10-13

    m = 2 x 4 x 10-13 /(V2 )

m = 2 x 4 x 10-13 /(8.33 x 106)2

m = 1.15 x 10-26 kg

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