5/12 Motors and Magnetic Fields

Purpose: Today we will explore magnetic fields and motors. We will learn how a magnetic is orientated and why. We will also find the relationships between magnetic fields and torque, as well as current. Our studies will also include motors.

We began class with the study of magnetic fields. We were given the following scenario: if given two pins, one is magnetized and the other isn't, how would their domain be orientated?

We found that the magnetized pin is orientated in straight lines (pictured below) and the reason this works as a magnetic is because positive and negative are orientated next together; negative will never have contact with another negative and the same concept applies to the positive charge. The non magnetized pin is orientated randomly(pictured below) so charges of the same type come in contact and cancel each other out causing to be non-magnetic.

We continued our discussion with the destruction of magnetics. We were asked, "What are two ways to destroy a magnet?" 

We answered: by heat and hitting it with a hammer 

Pictured below is professor Mason heating up a magnetized pin, after heating it up with a blow torch for a while it got so hot that it was no longer magnetic. This happens because originally the magnetic pin has its domain orientated in straight lines with opposite charges touching, however, once this is heated the electrons gain kinetic energy and become randomly orientated causing the pin to become demagnetized. (pictured below)

Torque On A Current Loop In A Uniform B-Field
For our next activity we were asked the following:
Calculate the torque on the rectangular current loop above for a rotation axis that is parallel to the x-axis and lies in the center of the loop.

Here we have our derivation for torque on a current loop with uniform magnetic field.

Torque on a current loop

A current loop in a magnetic field can experience forces on its sides which can generate a torque. We found that is a magnetic field is going through a loop, for example, a rectangular one, and B is coming from the left, then the top and bottom of that rectangle have no forces acting on it because they are parallel to the magnetic field (B).  Then say that their is a force on the left side going up and a force on the right side going down, then there is torque acting on the loop. Below is a picture of some of our equations, for torque which we did in class.

The bottom part of the picture above shows the example problem we did in class which is as follows:
Example:A 20-turn circular loop of wire of radius 4 cm carrying a current of 5 A is placed in a magnetic field of 0.1 T.  The angle between the field direction and the plane of the loop is 30^o.  Find the torque on the loop.

We calculated torque to be 0.044Nm but the correct answer was 

The reason we got the wrong answer is because we were using the wrong angle. We were given 30 degrees but in actually we had to subtract that 30 from 90 because then that would give us the angle between the normal to the plane and the field of direction.

The next question we were asked was, "What is the torque on a 50- loop of coil of radius 1.00-m in the next problem?" ( pictured below). First we found mue by multiplying the number of loops, current, and area of the circle together. After solving for mue, we used our torque equation mue cross the magnetic field and found our answer to be 600pi Newton Meters.

For our next discussion, we were shown the inside of small motors. We seen their frame work, such as their coils and commutator (pictured below).

Here we were asked what two things were more likely to break. We said coils and commutator, the others listed above were added once we had our discussion in class.

In our next activity we discussed the effects on a compass from a metal pole with current running through it. In this activity, the compasses are initially pointing north(as they should be). Professor Mason then placed the compasses around the metal pole and turned on the current so that it could run through the pole. The result was that the compasses started pointing in a circular direction (pictured below). We found that it was creating a circular magnetic field.

He then reversed the current which caused the compasses to point in a opposite circular direction.

This is our 2D interpretation of the activity we conducted with the compasses.



This next demonstration is about superposition, and how it can be used to treat magnetic fields. The board pictured below is an example of this. Magnetic field is created around a current carrying conductor.

Here professor Mason is running a compass over the current induced magnetic wire, in order to see which way it points.

My group drew a detailed picture of the magnetic field, current and compasses. We found that when two magnetic fields are next to each other and going in opposite directions, they cancel each other out.

We then conducted the experiment above by deriving the formula for magnetic force using Biot Savart Law
which is

Pictured below is our deviation for magnetic field. Which we found to equal mue divide my 4pin multiplied by electric charge and that mulitiped by the velocity vector and the cross product of that with the vector of the radius, all divide by the  radius squared.

For our last derivation, we were given this: 

Two  protons  move  parallel  to  the  x-axis  in  opposite  directions at the same speed v (small compared to the speed of light c). At the instant shown, compare the magnitude of the electric and magnetic force on these two particles. 

After find the ratio of the magnetic force and electric force, we derived an equation relating the two. Which is that it equal velocity square divided by c squared, c being the speed of light

Lastly we studied Ampere's Law given by:

It is said that Ampere's law is a magnetic field equivalent to Gauss's Law for electric field, and this law states that if the closed path contains any current caring wires then the results of integration is equal to the total current enclosed in path of integration. This law make finding highly symmetric charge distributions possible.