Experiment 8: Cyclotron motion of the charged particle in magnetic field Theory A charged particle moving in a magnetic field experiences a magnetic force FM  of magnitude given by   FM=qvBsinθ   where q  is the charge on the particle, v  is the magnitude of the particle velocity, and B  is the magnitude of the magnetic field

Experiment 8: Cyclotron motion of the charged particle in magnetic field

Theory

A charged particle moving in a magnetic field experiences a magnetic force FM

 of magnitude given by

FM=qvBsinθ

where q

 is the charge on the particle, v

 is the magnitude of the particle velocity, and B

 is the magnitude of the magnetic field. This force is perpendicular to both the velocity of the particle v and the direction of the magnetic field B. The direction of the force can be found from the Oersted right-hand rule.

Magnetic field cannot speed up or slow down a charged particle because the magnetic force is always perpendicular to the particle direction of motion. It will only cause the particle's path to curve because the velocity will change direction but not magnitude. In the case θ=90°

, the charged particle moves in the plane perpendicular to the magnetic field, and the magnetic force is equal to

F=qvB

It follows from Newtonian mechanics that a mass which experiences a constant force perpendicular to its velocity will move in a circle such that the force is directed toward its center. From Newton's Second Law for uniform circular motion it follows that

                                                                                  qvB=mv2Rc

                                                                           (1)

where Rc

 is the radius of the circle.  Uniform circular motion of the charged particle in perpendicular magnetic field is called the cyclotron motion and the radius of the circle Rc

 is called the cyclotron radius. Equation (1) describing this motion is called the cyclotron equation.

The goal of this lab to explore experimentally the cyclotron motion.

Procedure

Physics Simulations: Charged Particle in a Magnetic Field

https://ophysics.com/em7.html

PART A

Experiment

Set q=1×10-16

 C, m=1×10-25

 kg, and B=4

 T.

1. Shoot the charged particle into the magnetic field region with velocity v=5×106

   

    m/s and observe its motion in a semi-circular path until it leaves the magnetic field region.
2. Find the cyclotron radius Rc

   

    from your experiment and enter the experimental value into the data table.
3. Calculate the cyclotron radius Rc

   

    from equation (1) and enter the theoretical value into the data table.
4. Repeat this procedure for five more values of the velocity v

   

    shown in the table.

v  (m/s)	5×106	6×106	7×106	8×106	9×106	10×106
Rc , exp.
Rc , theor.

Analysis

1. Based on your experimental and theoretical data, how the cyclotron radius depends on the magnitude of the particle velocity?

2. Change the charge sign to opposite (negative) and observe how the particle path changes. Describe and explain the observed changes.

PART B

Experiment

Set q=2×10-16

 C, m=1×10-25

 kg, and v=5×106

m/s.

1. Shoot the charged particle into the magnetic field region with magnetic field B=1

   

    T and observe its motion in a semi-circular path until it leaves the magnetic field region.
2. Find the cyclotron radius Rc

   

    from your experiment and enter the experimental value into the data table.
3. Calculate the cyclotron radius Rc

   

    from equation (1) and enter the theoretical value into the data table.
4. Repeat this procedure for five more values of the magnetic field B

   

    shown in the table.

B  (T)	1	2	3	4	5	6
Rc , exp.
Rc , theor.

Analysis

1. Based on your experimental and theoretical data, how the cyclotron radius depends on the magnitude of the magnetic field?
2. Change the magnetic field direction to opposite (negative) and observe how the particle path changes. Describe and explain the observed changes.