You are asked to build a velocity selector for alpha particles (He nuclei) and y
ID: 2075399 • Letter: Y
Question
You are asked to build a velocity selector for alpha particles (He nuclei) and you are given a 0.7 T magnet to do that. a. If the magnetic field is pointing toward the positive direction of the y axis and the alpha particles are moving in the positive direction of the x axis, what should the direction of the electric field be? b. What is the magnitude of the electric field needed to make alpha particles, with a speed of 2.3 times10^5 m/s, move in straight line? c. Alpha particles moving at 2.3 times10^5 m/s leave the velocity selector to enter a region with a magnetic field of 0.5 T perpendicular to the direction of motion of the particles, what is the radius of the semicircular path they follow in this region? What is the cyclotron frequency for these particles?Explanation / Answer
(a). electric field is along negative Z direction.
(b).Magnetic field B = 0.7 T
Speed v = 2.3 x10 5 m/s
In velocity selector , Bvq = Eq
v = E / B
From this magnitude of electric field E = vB
E = (2.3 x10 5 )(0.7)
= 1.61x10 5 N/C
(c).Magnetic field B ' = 0.5 T
In magnetic field B ' ,
B ' vq = mv 2/ r
B' q = mv / r
From this radius r = mv /B ' q
r = (4x1.67x10 -27 kg)(2.3 x10 5 m/s)/(0.5 T)(2x1.6x10 -19 C)
= 9.6025x10 -3 m
We know B' q = mv / r
= m(rw) / r
= mw
From this angular frequency w = B ' q / m
w = (0.5)(2x1.6x10 -19 )/(4x1.67x10 -27)
= 23.952x10 6 rad/s
Frequency f = w/2(pi)
= 3.812x10 6 Hz
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