5/19 Electromagnetic Induction and Induction

Today we explored electromagnetic induction and induction. Using active physics we were able to get a better understanding of how they work.




We began with the study of magnetic flux and induced EMF. Using active physics, we seen the when there is a big change in magnetic flux, the induced EMF is just as big. We also concluded that negative EMF means there is a positive change in magnetic flux.

Our next assignment is a copper rod given current. We were asked to predict in which direction the copper rod would move when given current. 

What we found is that when we gave the rod a certain current, the rod would move in the direction of that current. However, when we changed the direction of the current, the rod moved in the opposite direction. This is because the current through the rod is going through a magnetic field (pictured above) which causes a force. Knowing this we can predict in which direction the rod would move.

We continued class with the study of inductors. We we found that inductance is negative EMF over the change in current with respect to time. In addition, we see that voltage is equal to inductance multiplied by the change in current with respect to time.

We continue to do some derivations and we find that current is equal to capacitance times the change in voltage over time.

Using what we found above, we are able to find the relationship between EMF and flux. Using length, number of turns, and area. 

here we have the derivation for inductance which we will use for Inductancts of solenoid. 

Given a length, area and numbers of turns, we were able to calculate inductance of solenoid.

Here we derived units of inductance, which we found to be Henry's .

For our next activity, we were asked what the current would be in a circuit after  a significant  amount of time has passed.

We found that current would plateau and goes towards infinity (pictured above).

Using ActivePhysics, we continued our study of RL circuits, which are circuits that contain inductors and resistors. We found that a change in flux would induce EMF. We also concluded that when the switch was closed the EMF would go in the opposite direction and the induced EMF opposes EMF of the battery. We also seen that when time was increased the inductiveness increased. The results of our experiment are pictured above.

5/26 LR Circuits

We began class with the discussion of current verses time, and we found that as current changes over time it induces EMF in the inductor.

Our first activity is to calculate inductance given a number of turns in a coil, the area and resistance. We found the inductance to be 760 micro henry's. We also discussed engineering notation which uses 10^-6 for values.

Using the inductance we calculated above we were able to calculate resistance is an 18 gauge coil. Which resulted in .48 ohms.

Finally, using the inductance and resistance we were able to calculate our time constant, using the equation tao= L/R.

Using the oscilloscope, we experimentally calculated our inductance, which we used to compare to our theoretical value of 760 micro henry's.

Using the graph from the oscilloscope, we calculated our experiment inductance.

Our experimental value for inductance was 703 micro henrys. We had a 7.5 % error.

In our next activity, did a LR circuit problem, in which there are two resistors in parallel and one resistor is in series with an inductor. Using the inductor and resistor 1, we were able to calculate the the time constant using the time constant formula. Our time constant was 2.9E-4.

Using ohms law, we were able to calculate Imax, and used that to calculate the current (picture above).

Using the value for current from the pervious picture we were able to find the time.

5/14 Faradays Law and Lenzs Law

Purpose: Today will study Faradays Law and Lenzs Law. We will also cover flux 

through a loop and EMF. A little background on these laws are as follows: Faraday's la of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). Lenzs Law states: If an induced current flows, its direction is always such that it will oppose the change which produced it. Which means the the induced voltage and the charge in magnetic flux have opposite signs.

We began class with a demonstration. We have two wires with current passing through them (picture below). The wires begin to repel each other because they become magnetized by the magnetic field. However, when the current in one of the wires is reversed the wires get closer to each other.

We were then given a scenario: We were given two lines, in which each had current, magnetic field and a magnetic force. We predicted that the current would be flowing upward. Our conclusion to the question is picture below.

Professor Mason then conducted another experiment by creating alternating current using a power supply in two parallel lines. We found that there were no net forces acting on the system because of the alternating current (pictured below)

Mason then created this graph on logger pro for the experiment from above. This is the magnetic field with respect to time graph which shows us the behavior of the magnetic field due to alternating current.







We then continued class with our next experiment: The Magnetic field  At the Center of A Current Loop.
We were asked to find the proportionality of loops and magnetic fields by measuring the magnetic field by in increasing the number of loops. We measured the magnetic field of each increasing loop on logger pro and graph it. What we found was that  the number of loops and the current is proportional to the magnetic field, thus the more loops the greater the magnetic field. Our values and graph is pictured below.

Next we move to flux. Flux measures the number of magnetic field lines that pass perpendicularly through a surface. we were given a plane with surface area ab, we were told to find the magnetic flux through that surface. We found that when the magnetic field is parallel to the surface area, the magnetic flux is zero, and when it is perpendicular to the area then it is defined by the following equation:

Here we also see Flux through a loop: when both the direction and magnitude of the magnetic field does not change across the surface bounded by a closed loop, flux can be expressed by the bottom equation in the picture above.

We then continue our studies with the creation of current in a coil of wire using magnetic fields. Professor Mason then used a galvanometer and a magnet to cause magnetic fields to change which created current which could be seen on the meter. (Galvanometer pictured below).

We found four ways to maximize current on induced EMF, we said more loops on a coil, bigger loops by increasing Area, bigger magnet, and moving the magnet faster.

We concluded that current could be induced by in a coil by a changing magnetic field.

Next we move on to Lenz's Law.

Direction of the Induced emf: Lenz's Law

General statement:
The effect of the induced emf is such as to oppose the change in magnetic flux that causes the induced emf. 

Professor Mason then conducted another experiment with a transformer, which has the ability to produce different voltages. The current passed through the coils and the magnetic field was generated from the metal pole sticking out the middle of the transformer.

In the picture below, we can see that the metal ring around the black pole is levitating and the reason for this is that there is a  magnetic field generated from this pole causing the ring to move in the opposite direction. We then conducted another experiment but this time the ring had a gap in it, this made the current unable to flow, thus the magnetic field was also affected. There was no magnetic field so the ring did not move. (no picture)

In the pictures below, a piece of metal is placed on top of the magnet which caused the light bulb to light up. 

When the north pole of the magnet is going toward a loop, the flux increases and an another upward magnetic field is created causing a counterclockwise current. This causes an upward force.

For our next experiment we were given to scenarios,  a magnet was to be dropped down and aluminum tube then down a plastic tube. What we found was that the magnet traveled at a much slower rate when traveling down the aluminum tube.

We concluded that the magnet moved slower down the aluminum tube because the magnetic field created a magnetic force going up. Thus, the induced current generated a magnetic field which then created a force that opposed the induced EMF, which caused it to move at a slower rate.

We continued with a mathematical representation of Faraday's Law (pictured below)

We took our definition of EMF and magnetic flux through a single loop of coil, and derived Faraday's law relating to electro motive force to flux.

Finally, we ended class by taking a look at the EMF verses time and compared it to the magnetic field verses time, we seen that when magnetic field is at a low EMF is at a high and vice versa.

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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.