How Do You Build a Homemade Cyclotron with Household Materials?

[baileya]

Homework Statement

The two main concepts in this chapter are:
Moving charges create magnetic fields & Magnetic fields exert forces on moving charges. 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?

Finally, as viewed from above the electrons are moving counter clockwise. What direction is the magnetic field? What is the direction of the conventional current in the wire loop? When you answer this, be sure to provide enough description of the right hand rules.

Homework Equations

F=ILBsintheta
qvB=mV^2/r
B=(4pi x 10^-7)T x m/A
B=(4pi x 10^-7)I(N/L)

The Attempt at a Solution

I figured out the length of wire using V=IR.. R=8. then dividing it by 3 and multiplying by 1000ft to get 2666.7 ft or 812.9m

I also figured out the circumference of the circle with .5 radius and finally determined the magnetic field (49 mT)

I don't know what formula I'm supposed to use to determine the speed of electrons.

I know how to do the right hand rule though, so I'm good for that.

 

[anathema]

To determine the speed of the electrons, you can use the equation qvB=mV^2/r, where q is the charge of the electron, v is the speed, B is the magnetic field, m is the mass of the electron, and r is the radius of the circular motion. You can rearrange the equation to solve for v: v=√(qBr/m).

To find the potential difference required to generate that speed, you can use the equation V=mv^2/2q, where m is the mass of the electron, v is the speed, and q is the charge of the electron.

Remember to convert the units to SI units before plugging them into the equations.

Also, to determine the direction of the magnetic field and conventional current, you can use the right hand rules. For the magnetic field, point your thumb in the direction of the conventional current and your fingers will curl in the direction of the magnetic field. For the conventional current, point your index finger in the direction of the magnetic field and your middle finger will point in the direction of the conventional current.