Electron in magnetic field equation

In summary, the equation for the radius of curvature of a relativistic electron in a magnetic field is R = gamma * m * v / e * B, where gamma is the Lorentz factor, m is the rest mass of the electron, v is the velocity, e is the electron charge, and B is the magnetic field strength. This can also be simplified to R = 3.336 * E / B, where E is the electron's energy in GeV and B is in T. The concept of relativistic mass is not commonly used in physics.
  • #1
ireland01
17
0
equation for radius of curvature of relativistic electron in magnetic field?

is this correct:R = gamma * m * v / e * B

where gamma is lorentz factor, m is electron mass, v is velocity, e is electron charge and B is magnetic field strength.
 
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  • #2
I use this simplified formula (E is electron's energy)
[tex]
R (\textrm {in m})=3.336\;\frac{E (\textrm {in GeV})}{B (\textrm {in T})}.
[/tex]
 
  • #3
ireland01 said:
equation for radius of curvature of relativistic electron in magnetic field?

is this correct:


R = gamma * m * v / e * B

where gamma is lorentz factor, m is electron mass, v is velocity, e is electron charge and B is magnetic field strength. is m rest mass?
Yes, that's correct. The only difference between the relativistic and non-relativistic formulas is the gamma.

m is the rest mass of the electron. Whenever physicists refer to mass, they almost always mean rest mass. The concept of relativistic mass, while popular with the laypeople, is not a very useful one since it's basically equal to the relativistic energy.
 

What is the equation for an electron in a magnetic field?

The equation for an electron in a magnetic field is given by F = qE + qv x B, where F is the force experienced by the electron, q is the charge of the electron, E is the electric field, v is the velocity of the electron, and B is the magnetic field.

How does the direction of the magnetic field affect the force on an electron?

The direction of the magnetic field affects the force on an electron through the cross product of the velocity and the magnetic field. If the velocity and magnetic field are parallel, there will be no force on the electron. If they are perpendicular, the force will be maximum. The direction of the force is always perpendicular to both the velocity and the magnetic field.

What is the significance of the charge and mass of an electron in this equation?

The charge and mass of an electron are important factors in this equation because they determine the strength of the force experienced by the electron. The greater the charge or the velocity of the electron, the greater the force will be. The mass of the electron also affects its acceleration in the magnetic field.

Can this equation be used for other charged particles besides electrons?

Yes, this equation can be used for any charged particle as long as the charge and mass of the particle are known. However, the force experienced by the particle may be different depending on its charge and velocity.

What are some real-world applications of the electron in magnetic field equation?

This equation is used in many real-world applications, such as particle accelerators, mass spectrometers, and MRI machines. It also plays a crucial role in understanding the behavior of charged particles in space, such as electrons in the Earth's magnetic field.

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