## Wednesday, February 18, 2015

### Magnetism stuff

For our magnetism quizzam, how well do you know:

- where magnetism comes from
- magnetic domain concept
- magnetic forces on charges, current carrying wires
- cross products, RHR vs LHR, circular motion of particles
- velocity selector, mass spectrometer
- force between multiple wires
- Ampere's law (long wires, long cylinders, toroids)
- Biot-Savart law (point charges, straight wires, current loops)
- current densities and Ampere's law (uniform, NON-uniform)
- Hall effect concept

This post has quick links to a bunch of magnetism videos. There are good simulations on ActivPhysics, and lots of good examples in the book, old AP exams, Princeton Review, etc.

## Monday, February 16, 2015

### Ampere's law with NON-Uniform Current Density

Here is an example of how to do a worst case scenario with Ampere's law (for a long, straight wire): A NON-uniform current density flowing through the cross sectional area of the wire.

Current density is just the current / (cross sectional area the current flows through). If this flow is a function of the radius, then it is NON-uniform flow, and, like a non-uniform charge density for Gauss's law, we will need to integrate the current density function to find the current inside the region we want. It hopefully sounds worse than it is, so check out the video for an example. I hope it helps!

We have checked out magnetism in a big way the past couple weeks. We know that magnetic fields are strange and circulate around moving charges and currents. We know that magnetic forces are created by magnetic fields acting on moving charges and currents: F = qv x B and F = Il x B.

Because these forces are cross products, moving charged particles will be put into circular motion by the magnetic force, and we have used the flat-hand right-hand/left-hand rules to figure out the direction of the push. We have also seen a major application of these forces in velocity selectors and mass spectrometers.

We then worked on the fields and forces created between multiple parallel wires with currents. This is a nice application of combining Ampere's law with the RHR's and the magnetic force equation, F1 = (I1)l x B2 and F2 = (I2)l x B1.

We then got into the production of magnetic fields, using Ampere's law for three special, symmetric cases: long straight wires, long solenoids, and toroids. This is built upon the notion of a path integral, since magnetic fields follow either circular paths (straight wire and toroid) or a linear path (inside solenoid). With the 'long' approximations, we do not need to use calculus, and it is B*(length of path) = mu*I_inside.

Then we hit the most difficult portion of all this, with the Biot-Savart law. This is used to find the magnetic fields for every other case, and we focus on three: single moving charged particles, a loop of current (like in our lab) and a straight wire with ends.  We treat these cases as they really are - a bunch of moving point charges, where we add up all the little B-fields to get the total B-field, using integration. We also can use this to find the effects of multiple wires.

We even got into the worst-case example for Ampere's law of a NON-uniform current density in a wire, where we need to integrate to find the current inside a certain portion of the wire.

One last piece of the puzzle is the Hall effect. This is a phenomenon that happens when a material carrying a current is placed in a B-field (directed at an angle to the current flow), and the material is polarized due to the magnetic force on the current. That polarization of the material can be measured as a voltage difference, and if the material is known, the magnetic field strength can actually be measured (a so-called Hall probe).

There's quite a bit here for plain magnetism, so hopefully these videos are useful!

## Tuesday, February 10, 2015

For the 4 Chem-Phys classes, check out this introductory video on Ampere's law. We are getting into the production of magnetic fields. This is like Gauss's law, only for magnetism, and will be useful for three shapes: straight wires, solenoids, and toroids (i.e. donut-shaped device).

For AP Physics C, check out a video on how we will need to integrate electric fields to find voltages when we have layers of charge (like capacitors).

## Friday, February 6, 2015

### Information for Classes, Jan. 6, 2015

Happy Friday everyone! We are at our WYSE regional competition today.

For 4 Chem-Phys, start off with two videos on magnetic forces and an application of those forces. Take notes on magnetic forces on electric charges, and then mass spectrometers and velocity selectors. These will be useful (hopefully!) for the homework set. After the videos, please check out the multiple choice questions from the semester final, and you should do an error analysis while recalling first semester information. Solutions to the final are here.

For AP Physics C, check out two videos on finding the electric fields of NON-Gaussian objects. This will involve integration. One case will be for charged sticks (but with ends...a little closer to reality!), and a second case for a curved stick (part of a charged ring). Take notes, as the homework problems will involve these techniques. After the videos, please complete the lab on equipotential lines and the potential gradient (i.e. electric field). Turn those in before leaving. You can use computers to access the ActivPhysics simulation as needed.

Thanks, and enjoy the weekend!