### Experiment 7

#### The Motion of a Charged-Particle in a Magnetic Field

Objective:

The objective of this experiment is to measure the period of rotation and angular speed of a moving charged-particle in a magnetic field

Equipment:

A computer with Internet connection, a calculator, paper, and pencil

Theory:

When charge q of mass M moving at velocity v crosses a magnetic field B  perpendicular to its field lines, the magnetic field forces the charge to travel along a circular path of radius R given by

Cross multiplying yields:   RqB = Mv.    This may be written as:

(1)

In this formula, w is the angular speed (rad/s) of the rotating charge, q/M is the charge-to-mass ratio (C/kg), and B is the strength of the magnetic field in Tesla.

Procedure:

If you have not done so, you may need to add the following Website to your Java exception list: http://www.phy.ntnu.edu.tw/.   To do this, follow the path (Windows operating system),

Start → All Programs → Java → Configure Java → Security (use High) → Edit Site List … → Add → Type in the site URL (http://www.phy.ntnu.edu.tw/).

You should see a 3-D figure.  The magnetic field B is upward shown by a blue vector along the Positive Y-axis.  The electric field E is shown by a red vector along the positive X-axis.  In each case of this experiment, we will set the electric field components equal to zero because we are studying the motion of a charged particle in a magnetic filed only.

Above the coordinates system, spaces are provided to type in the desired values for Ex , Ey , and Ez .  Before setting them equal to zero, the drift velocity, Vi , or Vd ,  must be determined for each run.  If you hold the left click down and try to pull the tip of the Vd  vector, it will move and appears as a small red vector with a small head.  The magnitude of Vd can be read as Vi in the top left corner of the rectangle in which this 3-D diagram is.   As you move the mouse,  the values of the components of the velocity vector  Vi  change allowing you to set it at any desired value.

For each case of Table 1:

1) Adjust the value of Vd  or Vi as given in the Table 1 by the left click held down.

2) Select one value for q/M and one for B and type them in.

3) Set Ex = 0,  (Ey and Ez are already zero).

4) Click start.  You will see the time running If you measure time t of n rotations and then divide it by n, you will find the period of rotation, T.

5) since w = 2p/T, divide 2p by T to get the value for w .

6) This value of w is your measured value.  It must be very close or equal to the accepted value that you calculate from Formula (1) above.

7) Calculate a % error for each case.

Note: To completely reset the applet for each new case, you must click on refresh and refresh the screen.

Data:

Given and Measured:

Table 1

 Case Vd m/s B Tesla q/M C/kg t sec. n turns T = t /n Acceptedw = (q/M)B Measuredw = 2π/T % error 1 20.0 50.0 0.01 2 30.0 40.0 0.025 3 35.0 80.0 0.025 4 40.0 80.0 0.050 5 50.0 90.0 0.060

Calculations:

Comparison of the Results:

The accepted and measured values of w may be used to obtain a percent error.

Conclusion: To be explained by students.

Discussion:  To be explained by students.