A cyclotron is used to accelerate electrons. Electrons are released from rest ne

Question

A cyclotron is used to accelerate electrons. Electrons are released from rest near the center of the cyclotron. The amplitude of the voltage across the gap in the cyclotron is 20 V. The magnetic field in the cyclotron is 0.5 T. The cyclotron accelerates the electrons to a speed of 5 * 10^7 m/s. Find the cyclotron frequency. What is the radius of the largest semicircle that the electron traces out before exiting the cyclotron What is the kinetic energy of the electron when it exits the cyclotron How many semicircles does the electron trace out before exiting the cyclotron

Explanation / Answer

Voltage, v=20 v

Magnetic field,B=0.5 T

Speed of electron=5*107 m/s

frequency, f=qB/ 2pi m

f=1.6*10-19*0.5 /(2*3.14*9.1*10-31)=1.399*1010 Hz

radius,r=mvp/qB

r=9.1*10-31*5*107/1.6*10-19*0.5=5.687*10-4m

Kinetic energy,KE=(1/2)mv2=0.5*9.1*10-31*(5*107)2=1.137 *10-15 J

circumference=speed/frequency=5*107/1.399*1010=3.573*10-3m

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