Magnetic Field & Electron Speed

[baileya]

Homework Statement

You have decided to make a home made cyclotron (particle accelerator). You decide to use a household circuit use a 120V, 15 Amp circuit. If 14-gauge copper wire has a resistance per unit length of 3 ohm per 1000ft, what length of wire is required to limit the current to 15A?

Next, your "cyclotron" needs to have a region of constant magnetic field. To create this, you choose to wrap the wire in a circular loop of radius 0.5-m. What is the maximum magnetic field you can create? (you need to figure out the number of loops!)

Finally you inject the electrons into your cyclotron. What is the speed of the electrons if they move in a radius of 0.25-m? If the electrons started from rest, what potential difference is required to generate that speed?

Homework Equations

The Attempt at a Solution

Alright... so I figured out the first parts of the question (812.9 m wire length and magnetic field of 49mT for the r=.5 m wire) but when I tried to determine the electron speed I got a number that's greater than the speed of light.
I determined that the circumference is 1.57 m, which allows for 517 loops of wire. Then using B=(4pi x 10^-7)NI/2r I got that the magnetic field is 1.9 x 10^-2
This means that using v=rqB/m where r=.25m, q=1.6 x 10^-19, B=1.9 x 10^-2, and m=9 x 10^-31)
I got that the speed of the electron is 8.4 x 10^8 m/s
This is way too fast I'm assuming, so can somebody tell me where I went wrong.

 

[kristenj17]

how did you find the length?