You are asked to build a velocity selector for alpha particles (He nuclei) and 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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