Period of an Electron Around a Magnetic Field

In summary, the period of an electron's motion in a uniform magnetic field of 0.152 teslas can be calculated using the equation T = 2(pi) * M / Q * B, where M is the mass of the electron and Q is its charge. The radius of the electron's path is not needed and the speed of light is not a relevant factor in this calculation. The correct period of the electron's motion in this scenario is 2.35E-10 seconds.
  • #1
bleedblue1234
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Homework Statement



An electron enters a uniform magnetic field of 0.152 teslas such that the electron follows a circular path. What is the period of the electron's motion? Electrons have a mass of about 9.11 x 10-31 kilograms each. Hint: Since the radius of the electron's path is not given, it must cancel out of the equations.


Homework Equations



Fm = Q * V * B

F = M * A

A = V^2/r

V= 2(pi)r/T


The Attempt at a Solution



Q * V * B = M * A
Q * V * B = M * V^2/r
Q * 2(pi)r/T * B = M* V^2/r
Q * 2(pi)/T * B = M * V^2
(1.6E-19) * 2(pi)/T = (9.11E-31) * (3.00E8)^2
Solve for T
T = 1.86E-6 s
But it is wrong...
 
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  • #2
How can you use v=3.00E8? Electrons can't possibly travel at the speed of light, and even if they could, the question doesn't say that they do.

Try substituting 2(pi)r/T in the v on the right side as well. Better yet, cancel out one v in Q * V * B = M * V^2/r, then substitute 2pi*r/T into the remaining v.
 
  • #3
Cool got it... here is what I did if somebody else would like to see...

Q * V * B = m * v^2/r

Q * B = M * V / R

Q* B = M * (2(pi)r/T)/r

Q * B = M * (2pi)/T

T = 2(pi) * M / Q * B

I got 2.35E-10 seconds... worked great... thanks
 

1. What is the period of an electron around a magnetic field?

The period of an electron around a magnetic field refers to the amount of time it takes for an electron to complete one full orbit around the magnetic field. This period is influenced by the strength of the magnetic field and the energy of the electron.

2. How is the period of an electron around a magnetic field calculated?

The period of an electron around a magnetic field can be calculated using the formula T=2πm/eB, where T is the period, m is the mass of the electron, e is the charge of the electron, and B is the strength of the magnetic field.

3. What is the relationship between the period of an electron and the strength of the magnetic field?

The period of an electron is inversely proportional to the strength of the magnetic field. This means that as the strength of the magnetic field increases, the period of the electron decreases, and vice versa.

4. How does the period of an electron around a magnetic field affect its energy?

The period of an electron around a magnetic field is directly related to its energy. As the electron moves faster around the magnetic field, its kinetic energy increases, and its potential energy decreases.

5. What factors can affect the period of an electron around a magnetic field?

The period of an electron around a magnetic field can be affected by the strength of the magnetic field, the energy of the electron, and any external forces acting on the electron, such as electric fields or other magnetic fields.

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