# Thomson Charge Mass Measurement by sanmelody

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Physics 30 Unit III -                                        Name: _______

Thomson's Charge/Mass                                        Date: _______

Measurement
Accessing the Lab - Navigate to the learnalberta.ca site:

Search for "Mass to Charge" and the experiment will come
up.

Thomson's Charge/Mass Measurement simulates the deflection of a charged
particle when passing through perpendicular electric and magnetic fields,
and it determines the charge/mass ratio by varying the fields and observing
the corresponding deflections.

Part 1: Learning the Applet
In Thompson’s original experiment, he used the following manipulated variables which
we can manipulate in the applet:

   an electric field, E, provided by a parallel plate capacitor. By default, the electric
field is pointing upwards.
   a magnetic field, B, perpendicular to the electric field. By default, it is pointing
out of the screen/paper.
   a parallel plate length, L, (changed by clicking and dragging the y-axis)

Thompson also had a controlled variable, the distance between the capacitor and the
collecting screen (y-axis), D, which in this applet is always set as 150.0 cm.

Thompson did not have the values of velocity, mass or charge. These values are included
in the applet to illustrate the principles Thompson first worked out.

Play around with the applet for 5 minutes or so. See how varying different values causes
the charge to either move upwards or downwards through the parallel plates.

Pre-Lab Questions:

1. What directions are the magnetic and electric forces acting in in this applet? Explain
using principles learned in class. (2 marks)

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3/27/2011

2. Draw a free body diagram of the forces acting on the charged particle while it is in the
fields. (1 mark)

Part 2: Determining Velocity
In Thompson’s day, there was no reliable way to determine the velocity of the charge. He
used his knowledge of Newton’s Laws to determine this speed, and so will you!

1. Click “Reset”, then click “Data” to see your measurements. Click, “Hide Values”, and
pretend you didn’t just see what the velocity was. Adjust the length of the capacitor L to
300.0 cm.

2. Choose a B-value and change the settings on the applet. Record your B-value below.

3. Run the applet by pressing play. Note what happens: the particle is deflected by the
electric and magnetic fields. You can see the amount of deflection in cm on the data chart
on the applet. While keeping the B-value constant, vary the E-field until the deflection is
zero. Record the E-value needed to balance the B-field on the table below.

(Hint: using “Rewind” instead of “Reset” is a more efficient way of running multiple
trials”.)

4. Repeat steps 2 and 3 with two different B-field values. Note that the capacitor may not
produce enough electric field to balance all B-field values, so choose your B-fields
wisely. Record all data below. (2 marks)

Trial       Electric Field (V/m)            Magnetic Field (T)
1

2

3

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5. Using your free body diagram and knowledge of Newton’s Laws to determine the
velocity of the particle in each trial. (Show only sample calculations.) You can check this
velocity with the one given in the applet. (3 marks)

Part 3: Determining Charge to Mass Ratio
Normally, when we determine the charge to mass ratio, we set FB = Fc. This works on
paper, but in real life, it is very difficult to measure the radius that a tiny charge will
undergo circular motion in! Thompson had no way of taking this measurement. He did,
however, know all about projectile motion! From these principles, he determined (with a
nice bit of algebra) an expression for the charge to mass ration.

1. Recreate the same settings from your velocity selection portion of the lab. You will
need your calculated velocity in this section. The only change to make is to set the B-
field value to zero.

With no B-field to balance the E-field, the particle will accelerate through the capacitor in
projectile motion.

2. Press play and observe the motion of the particle. When the particle is in the electric
field, it experiences a force acting upwards on it from the electric field. The particle rises
in projectile motion. After the particle leaves the field, it travels in a straight line with a
constant velocity before hitting the y-axis.

Questions
1. Write an expression for the upwards acceleration of the particle in the electric field.
(HINT: F = ma) (1 mark)

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3/27/2011

2. Using your acceleration from question 1, write an expression for the vertical
displacement, dy1 of the particle when it is in the electric field. (HINT: use dy = vit +
1/2at2, call the time t1.) (1 mark)

3. Given that the displacement in the x-direction the particle travels through while in the
E-field is called L in the applet and that the initial velocity of the particle is vx, write an
expression for the time, t1, the particle is in the E-field. (HINT: is there any acceleration
in the x-direction?) (1 mark)

4. Substitute your expression for time from question 3 into your expression for dy1 from
question 2. Simplify if needed. (1 mark)

5. After the particle has left the E-field, it travels with a constant velocity. Write an
expression for the vertical displacement of the particle, dy2, after it leaves the E-field. Call
time t2. (1 mark)

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3/27/2011

6. Given that the displacement in the x-direction the particle travels through after leaving
the E-field is called D in the applet and that the initial velocity of the particle is vx, write
an expression for the time, t2 the particle takes to travel from the E-field to the y-axis. (1
mark)

7. Determine an expression for the velocity in the vertical direction, vy2, of the particle
after it has left the E-field. Use your acceleration expression from question 1. (HINT: use
simple v = at) (1 mark)

8. Substitute your expression for t2 from question 6 and for vy2 from question 7 and for t1
from question 3 into your expression for dy2 from question 5. Simplify if needed. HA HA
HA!!!(1 mark)

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3/27/2011

9. If all has gone well up to this point, you now have an expression for dy1 and dy2. The
sum of these displacements is the same as the value y on the applet! So you can add the
two displacements to find a master equation to determine charge to mass ratio!

Add your expressions for dy1 (question 4) and dy2 (question 8). Factor out of the
expression q/m and solve for q/m. Your final expression should be in terms of E, v, L and
D. (2 marks)

11. Using your velocity from the first section, and the values of E, L and D from the
applet, determine the charge to mass ratio of this particle. (2 marks)

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