Can the Velocity of an Electron be Determined by a Change in Potential Energy?

[ACLerok]

i am just wondering, is it possible to find the velocity of a single electron that is accelerated by a certain potential difference?

Also I am having trouble with this homework problem:
A coil with a magnetic moment of 1.40 A*m^2 is oriented initially with its magnetic moment antiparallel to a uniform magnetic field of magnitude 0.845T.

What is the change in potential energy of the coil when it is rotated 180 degrees so that its magnetic moment is parallel to the field?

I remember that antiparallel means when two vectors just have the same direction cept that they are opposite signs so wouldn't the change in PE just be 0?

I'm not too sure about that one.

 

[photon_mass]

anti parallel means perpendicular.

 

[thermodynamicaldude]

Yes. You can find the velocity of an electron accelerated through a particular potential difference.

Remember that:

potential differerence (aka voltage) * charge = Change in potential energy (U)...

Since you know the charge of an electron...you can simply multiply this by the potential difference to figure out the energy change.

KE = U
Now, since KE = 1/2 mv^2 ...you can plug in and solve for velocity.

 

[ACLerok]

anti parallel means perpendicular.

the problem states that what happens when it is rotated 180 degrees and it is parallel. if anti parallel meant perpendicular, then it wouldn't be parallel.

 

[kawikdx225]

Yes. You can find the velocity of an electron accelerated through a particular potential difference.

Remember that:

potential differerence (aka voltage) * charge = Change in potential energy (U)...

Since you know the charge of an electron...you can simply multiply this by the potential difference to figure out the energy change.

KE = U
Now, since KE = 1/2 mv^2 ...you can plug in and solve for velocity.

I was also interested in the speed of an electron due to it's voltage so I plugged your formula into mathcad and when I use a voltage of 1 million volts I get a velocity of 5.931X10⁸m/s. This is faster than the speed of light? What am I doing wrong?

 

[thermodynamicaldude]

Well...the method I just gave you is based on classical mechanics, which basically works ok for anything << speed of light. However, anything remotely close to the speed of light (such as something with a speed of 0.1c)...would require the relativistic definitions...

In classical mechanics:

KE = 1/2 mv^2

In relativistic mechanics:

M = rest mass

KE = (MC^2 * y) - (Mc^2)...

with y = 1 / sqrt. (1 - v^2/c^2)

 

[kawikdx225]

Well...the method I just gave you is based on classical mechanics, which basically works ok for anything << speed of light. However, anything remotely close to the speed of light (such as something with a speed of 0.1c)...would require the relativistic definitions...

In classical mechanics:

KE = 1/2 mv^2

In relativistic mechanics:

M = rest mass

KE = (MC^2 * y) - (Mc^2)...

with y = 1 / sqrt. (1 - v^2/c^2)

Thanks, I'll give that a try.

 

[ACLerok]

can anyone still help me with my second problem?