An alpha particle moving in the plane of the page (the x-y plane) with a speed o

Question

An alpha particle moving in the plane of the page (the x-y plane) with a speed of 4.00 times 10^6 m/s enters a region with a uniform magnetic field. The field is directed in the +y direction and has a magnitude of 2.75 T. When it enters the field, the velocity of the alpha particle makes an angle of 30.0degree with the positive x axis. As soon as it enters the field, is the particle deflected out of the page or into the page? What is the radius of the circle that is the projection of the trajectory in the x-z plane? How long does the particle take to go around the circle once? How many times does the particle go around the circle in a second? How far does the particle move along the y axis in the time it takes to go around the circle once?

Explanation / Answer

a. as the particle enters nto the field, as it is a + charge , deflection will ne into the page

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b. radius r = mv/qB

r = (1.67 *10^-27 * 4*10^6)/(1.6*10^-19 * 2.75)

r = 1.51 cm

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c.

time t = 2pim/qB

t = 2*3.14 * 1.67 *10^-27/(1.6*10^-19 * 2.75)

t = 2.38 *10^-8 secs

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d.

frequency f = 1/t

f = 1/(2.38 *10^-8)

f = 4.2*10^7 Cycles per sec

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e. Vertcal Distance Y = ut

Y = 4*10^6 * 2.38 *10^-8

Y = 9.52 cm

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