- #1
komodekork
- 17
- 0
So a electron moves in a circle with radius r in a magnetic field. What does that circle look like in the rest frame of the electron?
What is the shape of an electron's circular motion in a magnetic field?
- Thread starter komodekork
- Start date
In summary, the conversation discusses the path of an electron in a magnetic field and the appearance of this path in the rest frame of the electron. It is determined that in the rest frame, the path appears as a single point. The transformation from the laboratory frame to the rest frame is discussed, with the conclusion that there is an inertial frame in which the electron is at rest once per revolution, and in this frame the path appears as a cycloid. There is a question about whether this frame is reasonable, and it is determined that it is an extended cycloid.
- #2
DrGreg
Science Advisor
Gold Member
- 2,474
- 2,083
In the rest frame of the electron, the electron is at rest, so its path is a single point.
- #3
komodekork
- 17
- 0
So if I were to transform the coordinates of all the points on the circle in the laboratory frame by the Lorentz transformation to the rest frame of the electron, then they would all coincide with the origin of that frame?
- #4
- #5
komodekork
- 17
- 0
Maybe I should have made this more explicit. I'm talking about what would a circle with radius r in a frame S look like, in a frame S', who is the instantaneous rest frame of a particle moving on that circle in frame S. Does that make sense?
I guess my question is what would the transformation be if I want to go from the laboratory frame to a instantaneous rest frame of the electron? Just a boost parallel to the instantaneous velocity pluss a translation?
Couldn't I then just use this transformation on the parametrisation of the circle in S, to findthe corresponding curve in S'?
I guess my question is what would the transformation be if I want to go from the laboratory frame to a instantaneous rest frame of the electron? Just a boost parallel to the instantaneous velocity pluss a translation?
Couldn't I then just use this transformation on the parametrisation of the circle in S, to findthe corresponding curve in S'?
- #6
mfb
Mentor
- 37,264
- 14,098
This is the inertial frame you are looking for. It is just a boost (and I don't care about translations, as nobody defined a zero here).mfb said:
- #7
FAQ: What is the shape of an electron's circular motion in a magnetic field?
What is an electron in a magnetic field?
An electron in a magnetic field refers to the behavior of an electron when it is subjected to a magnetic field. The electron experiences a force, known as the Lorentz force, which causes it to move in a circular or helical path.
How does a magnetic field affect an electron?
A magnetic field affects an electron by exerting a force on it. This force depends on the strength of the magnetic field and the velocity of the electron. The direction of the force is perpendicular to both the magnetic field and the velocity of the electron.
What is the relationship between an electron's charge and its motion in a magnetic field?
An electron's charge and its motion in a magnetic field are directly related. The force exerted on an electron in a magnetic field is proportional to the electron's charge. This means that a stronger magnetic field or a higher charge will result in a greater force on the electron.
How does the direction of a magnetic field affect an electron's motion?
The direction of a magnetic field can affect an electron's motion in various ways. If the magnetic field is parallel to the electron's velocity, the electron will experience no force and continue in a straight line. If the magnetic field is perpendicular to the electron's velocity, the electron will move in a circular or helical path. The direction of the force also depends on the direction of the magnetic field and the velocity of the electron.
What are some real-life applications of the behavior of an electron in a magnetic field?
The behavior of an electron in a magnetic field has many practical applications. Some examples include magnetic resonance imaging (MRI) in medicine, particle accelerators in physics research, and magnetic compasses for navigation. Understanding the behavior of electrons in a magnetic field is also crucial for developing technologies such as electric motors and generators.