Magnetic flux density of a relativistic electron

In summary, magnetic flux density, also known as magnetic field strength, is a measure of the strength of a magnetic field at a given point. It is represented by the symbol B and is measured in units of tesla (T). The magnetic flux density of a relativistic electron can be calculated using the formula B = μ0I/2πr, where μ0 is the permeability of free space, I is the current of the electron, and r is the distance from the electron. A relativistic electron is an electron that is moving at a speed close to the speed of light, causing it to exhibit unique properties such as an increase in mass and energy. Compared to a non-relativistic electron, the magnetic flux density of
  • #1
The forgetful one
4
2
Homework Statement
Lorentz factor = 100, synctron radiation v=5 GHz
What is the magnetic flux density formula (Mag_flux_den), orbital frequency
Relevant Equations
I used the formula Mag_flux_den = (Omega(Mag_flux_den) * c * Mass_electron * Lorentz factor) / mass_electron
But I am getting 1.647e41 Gauss.

I am not sure what the correct formulas I should be using.
Can someone point me towards the correct formulas to use?
q = 1.602e-19C
mass_electron = 1.098e27
c = 3e8
Omega(Mag_flux_den) = 5GHz
Lorentz factor = 100
synchrotron radiation at frequency v = 5GHz

Mag_flux_den = (Omega(Mag_flux_den) * c * Mass_electron * Lorentz factor) / mass_electron
Mag_flux_den = (5000 x 3e8 x 1.098e27 x 100 ) / 1.602e-19 = 1.647e41 / 1.602e-19 = 1.028e60

I don't know what the orbital frequency formula is? but I think it might be Omega(mag_flux_den) = q x Mag_flux_den / mass_electron x c
 
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  • #2
Omega(Mag_flux_den) = (1.602e-19 x 1.028e60 ) / (1.098e27 x 3e8) = 5.223e9 Therefore, the orbital frequency is 5.223 GHz.
 

Related to Magnetic flux density of a relativistic electron

What is magnetic flux density?

Magnetic flux density, also known as magnetic field strength, is a measure of the strength of a magnetic field. It is represented by the symbol B and is measured in units of tesla (T).

How is magnetic flux density related to a relativistic electron?

Magnetic flux density is related to a relativistic electron because as an electron moves at relativistic speeds, it creates a magnetic field around it. The strength of this magnetic field, or magnetic flux density, is directly proportional to the velocity and charge of the electron.

What is the formula for calculating magnetic flux density of a relativistic electron?

The formula for calculating magnetic flux density of a relativistic electron is B = (μ0 * γ * q * v)/2πr, where μ0 is the permeability of free space, γ is the Lorentz factor, q is the charge of the electron, v is the velocity of the electron, and r is the distance from the electron to the point at which magnetic flux density is being measured.

How does magnetic flux density affect the motion of a relativistic electron?

Magnetic flux density can affect the motion of a relativistic electron by exerting a force on the electron, causing it to accelerate or change direction. This is due to the interaction between the magnetic field created by the electron and the external magnetic field.

What are some real-world applications of understanding magnetic flux density of a relativistic electron?

Understanding magnetic flux density of a relativistic electron has many real-world applications. For example, it is essential in particle accelerators and other high-energy experiments, as well as in the development of magnetic confinement systems for fusion reactors. It also plays a crucial role in the design of electronic devices, such as MRI machines and particle detectors.

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