PCS125 Physics: Charge To Mass Ratio
Objective & Background
The main purpose of this lab was to determine the charge to mass ratio of an
electron with the help of various sophisticated laboratory apparatus and compare it with the
accepted value of the charge to mass ratio. A tube filled with helium gas atoms are boiled off a
hot filament and then accelerated through two different a pre-determined potential differences of
150V and 300V respectively, into a vacuum. The electrons travel into a magnetic field created by
aluminum coils. The magnetic field causes the electrons to deviate from a straight line and
causes them to travel in a circular path. The electron’s charge to mass ratio is then calculated as
the velocity of the electron is known through the potential difference and the magnetic field
strength is also known (Ryerson Physics Department) In order to calculate the magnetic field
strength, the average radius of the coil was measured in meters and the number of loops in the
1 2
vs R
coil was also determined. The graph of B 2 was created in order to determine the charge
to mass ratio as it was represented by the slope of the graph. (Ryerson Physics Department)
1
,PCS125 Physics: Charge To Mass Ratio
Theory:
When an electron or any charged particle travels through a magnetic field, it encounters a
force which influences the path of the electrons. The force is given by the equation below:
(Serway)
⃗
F =q ⃗v × B (1)
Where F is the force experienced by the charged particle in Newtons, q is the particle’s
charge in Coulombs, v is the particle’s velocity in meters/second (m/s), and finally B is the
strength of the magnetic field that the particle goes through in Teslas. Force here is a vector
quantity and the direction is given by the right hand rule when taking the cross product of
q ⃗v ∧B .
In this laboratory experiment, the path of the electrons was observed as the electrons
were accelerated through a uniform magnetic that is perpendicular to the velocity of the
electrons. The force acting on the electrons will affect the path of the electrons and as a result the
electrons deviate from a straight line and starts to move in a circular path. The uniform magnetic
field is produced using a pair of Helmholtz coils, and the magnetic field strength is given by the
equation below:
8 μNI
B=
√125 a (2)
Where N is the number of turns in each coil (130), a is the mean radius of each coil in
−7 −1 −1
meters, I is the current passing through each coil in amperes and μ0=4 π × 10 Wb A m .
The speed of the electrons which are accelerated though a known potential difference, V
or voltage can be calculated from the equation below:
2
, PCS125 Physics: Charge To Mass Ratio
1
m v 2=eV (3)
2
Where m is the mass of the electron in kilograms (kg), v is the velocity of the electrons in
meters/second (m/s), V is the potential difference in volts and e is the charge of en electron in
Coulombs.
The altered circular path of the electrons due to the magnetic field has a radius given by
the equation below:
mv
R= (4)
eB
By putting equations (3) and (4) together the newly formed equation is as following:
e 3
( )R
1 m
= (5)
B2 2V
The newly formed equation can be used to determine the charge to mass ratio of an
electron. (Ryerson Physics Department)
3
Objective & Background
The main purpose of this lab was to determine the charge to mass ratio of an
electron with the help of various sophisticated laboratory apparatus and compare it with the
accepted value of the charge to mass ratio. A tube filled with helium gas atoms are boiled off a
hot filament and then accelerated through two different a pre-determined potential differences of
150V and 300V respectively, into a vacuum. The electrons travel into a magnetic field created by
aluminum coils. The magnetic field causes the electrons to deviate from a straight line and
causes them to travel in a circular path. The electron’s charge to mass ratio is then calculated as
the velocity of the electron is known through the potential difference and the magnetic field
strength is also known (Ryerson Physics Department) In order to calculate the magnetic field
strength, the average radius of the coil was measured in meters and the number of loops in the
1 2
vs R
coil was also determined. The graph of B 2 was created in order to determine the charge
to mass ratio as it was represented by the slope of the graph. (Ryerson Physics Department)
1
,PCS125 Physics: Charge To Mass Ratio
Theory:
When an electron or any charged particle travels through a magnetic field, it encounters a
force which influences the path of the electrons. The force is given by the equation below:
(Serway)
⃗
F =q ⃗v × B (1)
Where F is the force experienced by the charged particle in Newtons, q is the particle’s
charge in Coulombs, v is the particle’s velocity in meters/second (m/s), and finally B is the
strength of the magnetic field that the particle goes through in Teslas. Force here is a vector
quantity and the direction is given by the right hand rule when taking the cross product of
q ⃗v ∧B .
In this laboratory experiment, the path of the electrons was observed as the electrons
were accelerated through a uniform magnetic that is perpendicular to the velocity of the
electrons. The force acting on the electrons will affect the path of the electrons and as a result the
electrons deviate from a straight line and starts to move in a circular path. The uniform magnetic
field is produced using a pair of Helmholtz coils, and the magnetic field strength is given by the
equation below:
8 μNI
B=
√125 a (2)
Where N is the number of turns in each coil (130), a is the mean radius of each coil in
−7 −1 −1
meters, I is the current passing through each coil in amperes and μ0=4 π × 10 Wb A m .
The speed of the electrons which are accelerated though a known potential difference, V
or voltage can be calculated from the equation below:
2
, PCS125 Physics: Charge To Mass Ratio
1
m v 2=eV (3)
2
Where m is the mass of the electron in kilograms (kg), v is the velocity of the electrons in
meters/second (m/s), V is the potential difference in volts and e is the charge of en electron in
Coulombs.
The altered circular path of the electrons due to the magnetic field has a radius given by
the equation below:
mv
R= (4)
eB
By putting equations (3) and (4) together the newly formed equation is as following:
e 3
( )R
1 m
= (5)
B2 2V
The newly formed equation can be used to determine the charge to mass ratio of an
electron. (Ryerson Physics Department)
3
