More on Magnetic Fields Prof Wolf 5/14/2014

Today we had a sub.... Professor Wolf!!  He's super cool we get to take three breaks instead of just one...  After the fiesta, we started a lecture of the Biot Savart Law, an equation describing the magnetic field generated by an electric current.

 Biot Savart Law of an infinite long uniform wire

Our group derivation about the center of a current-running square 

Biot Savart Law of a point at the origin of an uniform ring

Our group derivation by Dez about the center (left) about the edge (right)

Fan-shaped derivation as parallel components at each ends cancel out

Our first lab of the day involves the way to measure Earth's magnetic field inside our classroom:

The magnetic field of the earth was experimentally determined by applying a current to a coils and using the coils magnetic field. B(coil)=ulN/2R=B(earth)tan(theta). For B(coil) was determined Biot-Savart Law and a graph of the B(coil) vs tan(theta) created a slope that represents B(earth). The angle made when the current was applied was used to calculate tan(theta).

 Eath Magnetic Field Lab instructions 

Lab result including the experimental set up. 

After fitting the equation to our plotted points we observed that the magnetic field of the earth is approximately 2.83*10^-5 T.  As seen in the graph, our magnetic fields from each trial were not far to the order of Earth's magnetic field range from 25 to 65 microtesla.  Our major source of error was the angle theta used and the interference of Building 60's metal structure.

Next, more derivation of Biot Savart Law involving a point a distance away from a ring

Prof Wolf demonstrate the direction of the force vector by applying the right-hand rule

Then, we were introduced to the solenoid, a stack of current loops

Derivation of solenoid formulas

Prof Wolf measured the magnitude of the magnetic field inside springy solenoid coil spread out and connected to an energy source to provide it with a current.  By using a probe with Logger Pro, 

Last, we observed that the direction of magnetic field within the solenoid is equal to the solenoid's vector magnetic moment for a single current-carrying loop. The field is strongest at the center of the solenoid and drops off near the ends.  Due to this solenoid length in comparison to its diameter, it is long and the the magnetic field at each end is half as the magnitude at the center, as shown by Prof Wolf.