electromagnetism homework help
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Before You Begin
In the past few labs, you have investigated electric and magnetic fields. Your task for this lab is to take what
you have learned about electric and magnetic fields to investigate their effects on charged particles. You will
then apply what you learn to explore how a mass spectrometer works.
Discussion Questions
While your lab report is an individual assignment, remember that part of your grade for the week is to
participate in Discussions on Canvas with your group members. You are encouraged to discuss any part of
this week’s lab/concepts. You may also want to discuss the following practice problems and questions:
1. How could you tell whether moving electrons in a certain region of space are being deflected by an
electric field or by a magnetic field (or by both)?
2. Is there a way for 2 particles of different mass to undergo the same path and land at the same place in
a mass spectrometer? How?
Task #1: Electric Fields
For Task #1, you will review the behavior of a charged particle in an electric field.
A. Go to http://physics.bu.edu/~duffy/HTML5/charge_in_EField.html. This simulates a charged
particle being launched horizontally into a uniform electric field that is directed down. The sliders
allow you to adjust the strength of the electric field as well as the charge on the particle. Gravity is
neglected in this simulation. Try it with a few charge and field values.
a. Describe what will happen to a charged particle if it suddenly finds itself in the presence of a
uniform electric field.
B. As a charged particle passes through an electric field, it passes through a potential difference ∆V.
How do you know this statement is true? Explain.
C. If a charged particle starts from rest and passes through a potential difference ∆V, what is its change
in kinetic energy? Write an equation relating these quantities. Be sure to identify and define all
variables in your expression.
D. From the expression you found in Task #1-C, how would the kinetic energy of 2 charged particles of
different mass compare? How would their velocities compare?
Task #2: A Charge in a Magnetic Field
For Task #2, you will review the behavior of a charged particle in a magnetic field.
A. Go to http://physics.bu.edu/~duffy/HTML5/charge_in_field.html. This simulates a charged
particle in a uniform magnetic field. You can start the particle from rest or give it some initial
velocity either parallel or perpendicular to the magnetic field. You can also see simultaneous
particles of different charge and different velocities. Try out the different variations.
a. Describe what will happen to a charged particle at rest if it suddenly finds itself in the
presence of a uniform magnetic field.
b. What will happen to a charged particle moving with velocity v if it enters a uniform
magnetic field?
B. What is the equation representing the force on a moving charged particle by a magnetic field of
magnitude B? If this force can cause the particle to move in a circle, and the acceleration of particle
undergoing circular motion is 𝑎 =
𝑣
2
⁄
, use Newton’s second law to relate the force from the
𝑅𝑝𝑎𝑡ℎ
magnetic field to this acceleration.
C. Using the expressions, you derived in Task #2-B, derive an equation relating the speed of the
charged particle, v, the strength of the magnetic field, B, and the radius of the circular path, Rpath.
How does Rpath depend on the mass of the charged particle?
Task #3: Combining E and B
For Task #3, you will investigate the behavior of a charged particle simultaneously in electric and magnetic
fields.
A. Based on your knowledge of how a charged particle behaves in electric and magnetic fields, what
would happen to a particle if it is suddenly in a uniform electric field and a uniform magnetic field at
the same time? What if it starts at rest?
B. Consider a situation where a particle of charge q enters a region where a uniform magnetic field B
points into the page and a uniform electric field E points from the top plate to the bottom one like in
the figure below.
+ + + + + + + + + + + + +
E
B (into page)
– – – – – – – – – – – – – – –
a. How would the directions of the forces on the particle from the B and E fields compare?
b. Without changing the E or B fields, how can you ensure there is no net force on the
particle?
Task #4: The Mass Spectrometer
In Task #4, you will put everything together to create a mass spectrometer. Mass spectrometers have been
used for over a century to measure the mass of atoms and to identify different isotopes of the same element.
A. Go to http://physics.bu.edu/~duffy/HTML5/mass_spectrometer.html. This is a simulation of a
mass spectrometer. It is composed of three separate regions.
a. The first region is the accelerator. Here after the charged particles are produced, they are
subject to a uniform electric field which accelerates them through the slit into the next
region. How does changing the magnitude of the field affect the particle? Does this agree
with what you said in Task #1?
b. The second region is known as the velocity selector. This section only allows particles that
have a certain velocity pass through the slit on the other side. Try adjusting the velocity.
What else changes? What happens to particles that are traveling too fast? Too slow? Why
would we want the particles going into the mass separator to have the same velocity?
c. In the final region there is only a magnetic field so the ions that enter follow a circular path.
The radius of that path can be measured because the ions enter through a slit and then strike
and darken a photographic plate or some other kind of spatial detector. Assuming the
particles in the simulation have a positive charge, which direction is the magnetic field
pointing?
B. Derive an expression for the mass of a particle that makes it through the mass spectrometer as a
function of: charge, q, the path radius in the mass separator, Rpath, the magnetic field in the velocity
selector, B1, the electric field in the velocity selector, E, and the magnetic field in the mass separator,
B2.
C. Now that you can identify different masses, consider the following problem. Carbon atoms of
atomic mass 12.0 u are found to be mixed with another, unknown, element. In a mass spectrometer,
the carbon traverses a path of radius 22.4 cm and the unknown’s path has a 26.2 cm radius. What is
the unknown element? You may assume they have the same charge.
Wrap-Up
• Don’t forget to write your Implications section!
• Submit your individual lab report on Canvas. (Make sure to upload all relevant files.)
References
The simulations used in this lab are works by Andrew Duffy and are licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 International License.
Before You Begin
In the past few labs, you have investigated electric and magnetic fields. Your task for this lab is to take what
you have learned about electric and magnetic fields to investigate their effects on charged particles. You will
then apply what you learn to explore how a mass spectrometer works.
Discussion Questions
While your lab report is an individual assignment, remember that part of your grade for the week is to
participate in Discussions on Canvas with your group members. You are encouraged to discuss any part of
this week’s lab/concepts. You may also want to discuss the following practice problems and questions:
1. How could you tell whether moving electrons in a certain region of space are being deflected by an
electric field or by a magnetic field (or by both)?
2. Is there a way for 2 particles of different mass to undergo the same path and land at the same place in
a mass spectrometer? How?
Task #1: Electric Fields
For Task #1, you will review the behavior of a charged particle in an electric field.
A. Go to http://physics.bu.edu/~duffy/HTML5/charge_in_EField.html. This simulates a charged
particle being launched horizontally into a uniform electric field that is directed down. The sliders
allow you to adjust the strength of the electric field as well as the charge on the particle. Gravity is
neglected in this simulation. Try it with a few charge and field values.
a. Describe what will happen to a charged particle if it suddenly finds itself in the presence of a
uniform electric field.
B. As a charged particle passes through an electric field, it passes through a potential difference ∆V.
How do you know this statement is true? Explain.
C. If a charged particle starts from rest and passes through a potential difference ∆V, what is its change
in kinetic energy? Write an equation relating these quantities. Be sure to identify and define all
variables in your expression.
D. From the expression you found in Task #1-C, how would the kinetic energy of 2 charged particles of
different mass compare? How would their velocities compare?
Task #2: A Charge in a Magnetic Field
For Task #2, you will review the behavior of a charged particle in a magnetic field.
A. Go to http://physics.bu.edu/~duffy/HTML5/charge_in_field.html. This simulates a charged
particle in a uniform magnetic field. You can start the particle from rest or give it some initial
velocity either parallel or perpendicular to the magnetic field. You can also see simultaneous
particles of different charge and different velocities. Try out the different variations.
a. Describe what will happen to a charged particle at rest if it suddenly finds itself in the
presence of a uniform magnetic field.
b. What will happen to a charged particle moving with velocity v if it enters a uniform
magnetic field?
B. What is the equation representing the force on a moving charged particle by a magnetic field of
magnitude B? If this force can cause the particle to move in a circle, and the acceleration of particle
undergoing circular motion is 𝑎 =
𝑣
2
⁄
, use Newton’s second law to relate the force from the
𝑅𝑝𝑎𝑡ℎ
magnetic field to this acceleration.
C. Using the expressions, you derived in Task #2-B, derive an equation relating the speed of the
charged particle, v, the strength of the magnetic field, B, and the radius of the circular path, Rpath.
How does Rpath depend on the mass of the charged particle?
Task #3: Combining E and B
For Task #3, you will investigate the behavior of a charged particle simultaneously in electric and magnetic
fields.
A. Based on your knowledge of how a charged particle behaves in electric and magnetic fields, what
would happen to a particle if it is suddenly in a uniform electric field and a uniform magnetic field at
the same time? What if it starts at rest?
B. Consider a situation where a particle of charge q enters a region where a uniform magnetic field B
points into the page and a uniform electric field E points from the top plate to the bottom one like in
the figure below.
+ + + + + + + + + + + + +
E
B (into page)
– – – – – – – – – – – – – – –
a. How would the directions of the forces on the particle from the B and E fields compare?
b. Without changing the E or B fields, how can you ensure there is no net force on the
particle?
Task #4: The Mass Spectrometer
In Task #4, you will put everything together to create a mass spectrometer. Mass spectrometers have been
used for over a century to measure the mass of atoms and to identify different isotopes of the same element.
A. Go to http://physics.bu.edu/~duffy/HTML5/mass_spectrometer.html. This is a simulation of a
mass spectrometer. It is composed of three separate regions.
a. The first region is the accelerator. Here after the charged particles are produced, they are
subject to a uniform electric field which accelerates them through the slit into the next
region. How does changing the magnitude of the field affect the particle? Does this agree
with what you said in Task #1?
b. The second region is known as the velocity selector. This section only allows particles that
have a certain velocity pass through the slit on the other side. Try adjusting the velocity.
What else changes? What happens to particles that are traveling too fast? Too slow? Why
would we want the particles going into the mass separator to have the same velocity?
c. In the final region there is only a magnetic field so the ions that enter follow a circular path.
The radius of that path can be measured because the ions enter through a slit and then strike
and darken a photographic plate or some other kind of spatial detector. Assuming the
particles in the simulation have a positive charge, which direction is the magnetic field
pointing?
B. Derive an expression for the mass of a particle that makes it through the mass spectrometer as a
function of: charge, q, the path radius in the mass separator, Rpath, the magnetic field in the velocity
selector, B1, the electric field in the velocity selector, E, and the magnetic field in the mass separator,
B2.
C. Now that you can identify different masses, consider the following problem. Carbon atoms of
atomic mass 12.0 u are found to be mixed with another, unknown, element. In a mass spectrometer,
the carbon traverses a path of radius 22.4 cm and the unknown’s path has a 26.2 cm radius. What is
the unknown element? You may assume they have the same charge.
Wrap-Up
• Don’t forget to write your Implications section!
• Submit your individual lab report on Canvas. (Make sure to upload all relevant files.)
References
The simulations used in this lab are works by Andrew Duffy and are licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 International License.
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