Bruce MacNicol
Alexander Dzuricky and Jasmyne Rogers
UNIV 150
10/23/2019
Electromagnetic Induction
Electromagnetic Induction is the idea that a magnetic field that is changing/moving over a wire can generate a current. The idea of this was first suggested by Michael Faraday. Prior to Faraday, the previously accepted model of electricity was to describe it like water flowing through a pipe, however there were some things that could not be described by the old model. Faraday explained the concept through something he called force lines, but we would call those field lines today. This is best explained with a simple experiment. If you had a coil of wire connected in a circuit with no power, and you move a magnet in and out of the coil, you will notice very little current is created. This is called an induced EMF, or electromagnetic force. This will only work if the current flows in a complete circuit, or else we will notice a build up of positively and negatively charged particles on opposite sides of the rod/ the ends of the circuit if it is not complete. We can predict the direction of the force, the current and the magnetic field by using Fleming’s Left Hand Rule, and Right Hand Rules(see url’s at the bottom for demonstrations of both the Left Hand Rule and the right hand rules). The observations made by German scientist Heinrich Lenz created Lenz’s law. Lenz’s law states that the direction of the induced EMF opposes the direction of the change that created the change. Lenz’s law is actually a consequence of Conservation of Energy. If it did not oppose the motion, then the magnet would then be attracted to the wire, meaning that it would begin accelerating faster and faster, meaning that it is gaining kinetic energy out of nowhere, violating conservation of energy.
Since this concept uses a magnetic field, we need to pull some previous knowledge. We know that the magnitude of a magnetic force is equivalent to BIl where B is the magnetic field strength, I is current and l is length. The energy we supply over a time t is equal to the force times the change in distance, or E=BIl*x and the induced emf is equal to the energy per charges, or EQ where Q is the number of charges in coulombs. Knowing that Q=It, the equation for the induced emf can change to BIl*xIt. Cancelling things out, we get the resulting equation: =Blv when a wire is moving through a magnetic field of constant magnetic field strength B, a wire length of l, and the speed of the wire being v. This can also be rewritten as =BAtA different term to be careful not to mix with the magnetic field strength is magnetic flux density. They are numerically equivalent, however are two very different terms. Magnetic field strength is a measure in newtons of the strength of a force at a certain point within the field, however Magnetic flux density is the measure of how many field lines fit through an area A. Magnetic flux density is also represented by the letter B, meaning you need to be careful when discerning between the two. Magnetic flux() is mathematically expressed as =BA. The  does not mean multiply in this case, it represents the cross product between the two. To fully represent that, the equation can be rewritten as =BAcos. The difference between flux density and flux is that the flux density is a measure of how many field lines flow through 1 square meter while flux is a measure of the total.
Going back to the equation, =BAt, that can be rewritten as =BAt=t. This means emf can be redefined as the change in magnetic flux over time. There is a separate concept to talk about within magnetic flux called magnetic flux linkage which is where there is more than one coil, meaning that the change is happening through multiple instances of the same thing. This adds an addition variable n to the equation for the induced emf, and going back up to Lenz’s Law, adds the final piece of the equation. The full equation for induced electromagnetic force is = -nt. This equation is also known as Faraday’s Law of Induction. We can use the basic concepts learned above for power generation and transmission.
To start off with power generation, we must talk about the difference between alternating current(AC) and direct current(DC). Alternating current is generated sinusoidally, meaning that the current flows both ways, while for direct current, the current is only one sided. Most of the power we generate is AC because it is significantly easier to make plus we can transport it very far distances. To generate AC, you need magnets, a coil/loop of wire, and slip rings. Using the idea that a change in magnetic flux over time creates in induced current, you rotate the coil of area A, and as the angle changes, so does that area/angle. This means that the current is more at certain points compared to others. AC is the main reason we describe electricity as a wave, because the way current is produced is a wave. The slip rings are used to keep the coil spinning yet be able to get the current out of the coil and out into a circuit. We measure the current produced in AC through the method of root means squared. Root means squared current is mathematically represented as 12Imax2. Logically this is because to get the average, you first need to square the output or else it would be 0. Once you square, you take half of the max value and square root it. To simplify, Irms=Imax2. Voltage is the exact same as current. I decided to spare you from that math.
	The main reason AC current is so common is because of a device called a transformer. A transformer is an input wire coiled around a taurus/soft iron core with an output wire coiled around it as well. As current flows through  the input wire (also called the primary coil), there is a magnetic field induced in the coil, which is transferred to the soft iron core, and then to the secondary coil. Using Faraday’s Law of Induction, we know that the more coils, the greater the induced emf which is the same as the voltage. This means that the ratio of coils is equivalent to the ratio of the input voltage over the output voltage. This does not violate the conservation of energy because the power from the magnetic field remains the same. Therefore, the current drops very low to compensate for the raise in voltage. This is used because Power dissipated in a wire is equal to Pd=I2R. This means that the lower the current, the less the power drops over time. This means that we can transport energy farther based on how much voltage the power carries. There is however an issue with an iron core within a transformer. The iron core is a great conductor meaning that the power created by the primary coil goes to these eddy currents rather than generating a current in the secondary coil. To counteract the eddy currents, we laminate the core, forcing the current to take longer routes without harming the magnetic properties of the iron.
Once we get the AC to the place we need it to be, we run into an issue. Most of the electronics we use, uses DC electricity. To convert from AC to DC, we must use a rectification circuit. A rectification circuit allows us to change the sinusoidal output of AC generation to a linear, positive output. For half wave rectification, we use only one diode. A diode is designed to only let current flow through it in one direction. This would end up making the negative portion of the output equal to 0. This means we are wasting half of the AC, and that is not good. To do a full wave rectification, we use a diode bridge which makes both sides of the sine graph flow on the same side. We do not get a consistent output from this however as it is still a wave. To fix that, we would add a capacitor to the full wave rectifier after the diode bridge. The capacitor would have a smoothing effect on the output.
A capacitor is two plates of area A separated by a distance d. We measure the capacitance that a capacitor can hold as c=0Ad where epsilon not(that curly e thing) is the permittivity of free space. That means how easy the electrons can travel between the plates. The way capacitors work in theory is that the negatively charged particles go to one side of the plates and the positive to the opposite plate creating a potential difference. When the power source is taken away, the capacitor “creates” a current from its stored energy. The energy within a capacitor exponentially decreases giving a capacitor a “half-life”. This is mathematically represented by the equation Q=Q0etwhere  is the time constant of the circuit. The time constant is not the same as the half life, but is equal to the resistance of the circuit times the capacitance. The epsilon not can change to epsilon if the circuit has a dielectric material. This means that the material in between allows for more stuff to move in between the plates when the power source cuts.
I hope you enjoyed your physics lesson :)

Links:
Right Hand Rule
https://www.khanacademy.org/test-prep/mcat/physical-processes/magnetism-mcat/a/using-the-right-hand-rule
Left Hand Rule
https://www.electrical4u.com/fleming-left-hand-rule-and-fleming-right-hand-rule/

Have fun generating your own power. Don’t forget your full wave rectification circuit.



Works Cited
Homer, David , et al. IB Physics Course Companion: 2014 Edition. Oxford University Press, 2014, pp. 427-469.