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:
click on http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=36.0 .
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 E_{x }, E_{y }, and E_{z } . Before setting them equal to zero, the drift velocity, V_{i }, or V_{d } , must be determined for each run. If you hold the left click down and try to pull the tip of the V_{d} vector, it will move and appears as a small red vector with a small head. The magnitude of V_{d} can be read as V_{i} 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 V_{i} change allowing you to set it at any desired value.
For each case of Table 1:
1) Adjust the value of V_{d} or V_{i} 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 E_{x} = 0, (E_{y} and E_{z} 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 | V_{d} m/s |
B Tesla |
q/M C/kg |
t sec. |
n turns |
T = t /n |
Accepted w = (q/M)B |
Measured w = 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:
Follow the steps under "Procedure."
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.