Determine Velocity of Electron in Magnetic Field

[Idea04]

What is an equation to determine the velocity of an electron moving parallel to a magnetic field? Or in other words in the same direction if the magnetic field.

 

[SpaceTiger]

What is an equation to determine the velocity of an electron moving parallel to a magnetic field? Or in other words in the same direction if the magnetic field.

$$\frac{d\vec{v}}{dt}=\frac{q_e}{m_e}\vec{v} \times \vec{B}$$

where $\vec{v}$ is the velocity of the electron, q_e is the electron charge, m_e is the electron mass, $\vec{B}$ is the magnetic field, and t is time.

Can you figure out what this equation reduces to if $\vec{v}$ is parallel to $\vec{B}$?

 

[Idea04]

Thanks for the equation. But I'm not that good at math. I don't know what d stands for and I don't have a value for the velocity. Can someone show me how to do the equation. qe electron charge is 1.60217646x10^-19 coulombs. me electron mass is 9.10938188x10^-31kg. t time is 1 second. B magnetic field is .000232496073 tesla's.

 

[Idea04]

Does anyone know how to do this equation? I want to know how to do it since I don't have the value for velocity and the value for d. And what do you do with the values on the other side of the = sign? Can someone please show me how this equation works out.

 

[Gokul43201]

The velocity of the electron has nothing to do with the magnetic field (in this case).

If this is a textbook or homework question, post the exact question (completely).

PS : What grade are you in, and where did this question come from ?

 

[Idea04]

It's not a textbook question. I'm not in school. I graduated a couple of years ago. Where i getting at is that an electron can be accelerated by a magnetic field. I'm trying to determine the speed of the electron by the strength of the magnetic field. Hence, an equation is needed to determine the velocity.

 

[rho]

Do you mean drift velocity in a wire?

 

[ZapperZ]

It's not a textbook question. I'm not in school. I graduated a couple of years ago. Where i getting at is that an electron can be accelerated by a magnetic field. I'm trying to determine the speed of the electron by the strength of the magnetic field. Hence, an equation is needed to determine the velocity.

Electrons cannot gain energy from magnetic fields, if that's what you mean. The only form of "acceleration" it can acquire from such fields is via a change in direction without a change in speed (as in a circular motion). Other than that, nope, no linear acceleration. It is why we use magnets in accelerators for focusing and steering, but use E-field in accelerating structures for accelerations.

Zz.

 

[Idea04]

You learn something new everyday. Well then if an electric field accelerates an electron how can you determine the speed of the electron with the strength of the electric field.

 

[ZapperZ]

You learn something new everyday. Well then if an electric field accelerates an electron how can you determine the speed of the electron with the strength of the electric field.

You use a bending magnet very mych like a "mass" spectrometer. The electrons having a higher kinetic energy will be bent less than the ones having a smaller kinetic energy. By calibrating the the magnetic field in the bending magnet, you can tell what the KE and thus, velocity of those electrons based simply on where they hit a detector.

Zz.