Induced Current

Purpose: In our experiments, we take a look at the effects of the change in the magnetic field. We will find that there are a wide variety of applications with the change in magnetic field.

The Force On Two Wires With Current

We begin by looking at how the two wires with current generate a magnetic field and this magnetic field influences the two wires by providing a magnetic force. We see that force is very small.

Induced Current

We set up a couple a wires connected to a machine that detects current. These wires a oriented in a loop or loops and we put a magnet inside the loops. We see that is the magnet just sits there, there is not current in the wires.

Professor Mason shows us that when we actually move the magnet through the loops, current is generated. This means that the change in the magnetic field induces current along the wire. Professor Mason demonstrates to us that the direction the magnet is moving or changing determines which way the induces current flows. 

Induced Current On A Coil Of Wire

We begin to apply the idea of induced current in a way the would help us to power a light bulb without a power supply connected directly to the loop of wires connected to the light bulb. We connect an AC power supply to a loop of wires which generates a magnetic field though the center. Since we are using an AC power supply, the current is always change causing the magnetic field to always change. This is essentially the same idea s moving the magnet back and forth. If we place the loop of wires that are connected to the bulb where the magnetic field changes, we can, essentially, induce current to power the light bulb without wires.

Induced Current On Metal Rings

We take another look into the induced current idea but see how this works with a metal ring. We find that current is induced in the ring in a similar fashion as the loops of wire that are connected to the light bulb. The current induced is in the opposite direction as the current in the loops underneath the current in the wire and, thus, generates a magnetic field in the opposite direction. This is the same idea as putting the same poles of two magnets together. They end up repelling but since the coil of wires connected to the power supply is fixed on the ground, the ring is the only thing that moves and it makes sense that is should move up.

We write four things on our whiteboard that can induce current. We can change the speed on the moving magnet, change the radius of the loops, increase the size of the magnet, or change the length of the wire.

Magnetic Race

Professor Mason shows us that a magnet going through a metal tube will induce current in the metal tube which will then generate a magnetic field. This magnetic field slows the magnet down significantly.

On our white board, we draw a representation of what is happening as the magnet is falling through the metal tube. We, also, write up a theoretical equation of the induced emf.

Conclusion:  The change in the magnetic field has a lot of practical use. We find the we can induce current in a loop of wire which could, ultimately, power a light bulb or charge and object. We take a look at how the current can generate a magnetic field around the wires which in turn creates a magnetic force on the wire next to it. We discussed how the current in a loop of wire creates a magnetic field at the center of the loop directed perpendicular to the circular plane. This is why our metal rings flew up. Finally, we discussed how a magnet through a metal tube feels a magnetic force from the induce current on the tube that generates a magnetic field.

Magnetic Fields Caused By Currents

Purpose:  We begin by look at the magnetic field generated by a wire with current. We, also, look into the effects of a current a wire in the presence of a magnetic field and how we can implement this with our electric motors.

Effects Of Heating A Magnetized Object

We discussed that there are two ways to demagnetize a piece of metal. One option was to simply hit the metal. The other option was to heat it until it is demagnetized. In some cases, like the video shows, demagnetizing an object may take a lot of heat.

On the right side of our white board, we indicate how magnets are magnetic and how objects that can become magnetic are not magnetic at the microscopic level. We drew little pill like figures that have their own poles and show how they are oriented when some object is magnetic and when some object is not. When something is magnetic, the poles all face in the same direction. We also discuss electric dipole moments, which is the potential for some some closed circuit to rotate with some torque.

Electric Motors

We begin to look at how electric motors work. We see that the rotation of the motors is dependent on the current in the wire, which is dependent on the the potential difference on the power supply. Our video shows that if we switch the wiring from the batteries. the current switches direction and the motor rotates in the opposite direction. This just proves that the magnetic force is dependent of the direction of the current and the direction of the magnetic field. The reason why the motor continues to rotate and not stop like in the previous lab is because the part of the motor that is allowed to rotate has a piece of circular metal at the center axis of rotation the is sliced in half. this means that they are essentially not connected. Each wire is connected to each slice and since the slice is made of metal, current is allowed to flow through it, as the motor rotates, the slices rotate as well and the fixed wires the touch the slices disconnect from the slice and proceed to touch the next slice. This causes the torque to remain in the same direction as long as current continues to flow out of the battery in the same direction.

Our next task was to create our own motor our of one magnet, a single wire, and some plugs to connect the single wire to the battery. We rolled the wire until it had a fair amount of loops and the loop was decently sized. This had to be accounted for because we know that the moment is dependent on the amount of loops as well and the area that the loops encompass.

In our whiteboard, we indicate how that magnetic field and the current effect the way the loop rotates on the motor used previously. The motor had two sides composed of loops and the current was flowing in the same direction. 

Looking At The Magnetic Field Around A Wire With Current

Professor Mason shows us that the current in a wire creates a magnetic field around in that flows in a circular motion around the loop. We find that we can use our right hand to find the direction that the magnetic field rotates by facing our thumb in the direction of the current. Our fingers end up showing the direction of the magnetic field. This is also shown using the magnets in the video.

Professor Mason demonstrates which direction the magnetic field is going in a wire that is positioned in an intricate way. We find that the magnetic forces can simply be added.

We discuss how the magnetic force and the electric force helps give rise to the speed of light constant. We also give a representative drawing of how the magnetic field rotates around a wire of current. The circle with a dot at the center shows us that the current is directed out of the board. We also start to get into Ampere's Law. This law allows us to find the magnetic field with the currents that generate the magnetic field. This law is very similar to the way Gauss' Law, which uses the charge to find the electric field.

Conclusion:  We discussed how heating up a magnetized metal can demagnetize it, It can also demagnetize with time and by striking the metal until it is demagnetized. We, also, discuss how we can create a loop of wire with current to rotate repeatedly so that we may use it as a motor. This is done by continuously changing the direction of the current of the loops so that it does not stop at 90 degrees like it did in the previous lab. Finally, we see that a wire with current also produces a magnetic field around the wire in a cyclone manner. We found that we can get the direction of the field using the right hand rule and that Ampere's Law makes it easy to find the value of the magnetic field.

Magnetic Field

Purpose:  We take a first look at how magnets behave and how the magnetic field lines look like. We will take a look at some of the fundamental principles of magnets and their relationships with moving charges. It will turn out that these guidelines will mirror what we saw in static electricity.

The Magnetic Field Lines Of A Magnet

Professor Mason shows us on a projector the behavior of the magnetic field lines on a magnet. This is done by using iron shavings. The iron shavings react to the magnetic field and basically give a visual representation of the magnetic field in 2-D. We see that the magnetic field, in a way, circles the magnet.

Our group makes an attempt on how these shavings look using arrows. This proves not to be a good representation for the magnetic field.

We alter the lines of the previous picture to give a better idea of how the magnetic field lines go on the magnet. The field lines actually create circular loops that go through the magnet. If the field lines go in one end of the magnet, they go out the other end. We call these ends, poles. One end is the North pole and the other end the South pole.

What Occurs When A Magnet Is Cut Into Two Pieces

When a magnet is cut into two pieces, we see that we do not create monopoles. Instead, the cut pieces because new magnets we north and south poles. Professor Mason demonstrates this by cutting a magnet.

Using Gauss' Law To Interpret Magnetism

We take a look at the idea used in Gauss' Law for drawing field lines to find the flux of the magnetic field. We see that the amount of lines that go out go back in. This means that the flux is always equal to zero.

Effects Of A Magnet On An Oscilloscope

Professor Mason demonstrates the effects a magnet has on an oscilloscope. We see the dot shift. The dot shifts according to the definition of the magnetic force, which is basically the cross product between the velocity the charge moves with the electric field.

We draw on our white board what occurs from a side view inside the oscilloscope. The horizontal line indicates the velocity of the beam. If we put a magnetic field across the beam, we can see that the force vector is perpendicular to the velocity vector and the magnetic field vector.

As an activity, we calculate the acceleration along the force axis. The cross product give us the force, and Newton's Second Law helps us attain the acceleration.

Motion Of A Moving Charge Under A Magnetic Field

Our board shows that if we have a charge moving at some velocity in a direction perpendicular to the magnetic field, the charge goes in a circular motion, as the force and the velocity continually changes.

Magnetic Force Along a Current

Professor Mason demonstrates that when we have a current running through a wire and this wires is exposed to some magnetic field, it will experience a force perpendicular to the length of the wire and the magnetic field.

After seeing the wire with current experience a force, we rewrite the equation for the force cause by the magnetic field in a way that describes a current carrying wire. The definition comes from the combination of the drift velocity and the number of charges contained within the wire. We run into the the definition for the current which replaces most of the variables that describe the wire.

Magnetic Force On A Circular Current

We see that if we have a circular current exposed to a magnetic field, the loop experiences a force that cause a torque. The loop does not continue to spin because after the loop rotates 90 degrees, the torque immediately goes the opposite direction. This cause the loops to spin 90 degrees and then stop.

The white board shows our prediction of what would happen to the loop when it experiences a magnetic field. We were right. We knew that there would be a counter torque, and while it is true that there is some angular momentum on the loop, the momentum is not large enough to keep the loop spinning.

Force On a Semicircular Loop

On excel, we are given the task to find the force that the loop experiences. We decide to approach the problem from a length of theta and calculate these individual forces. We know that the loop experiences the maximum force at the very top, as the vector length is perpendicular to the magnetic field. It has no force at the ends because the vector length is parallel to the magnetic field.

Calculating the different forces at different thetas gave us many forces in which we add to give us the net force that the loop experiences from the magnetic field.

Conclusion:  We discuss how magnetic fields behave and that there are no monopoles in existence. We also talk about how the movement of the charge and the direction of the magnetic field causes a force to be applied on the charge. This mirrors the ideas used in static electricity, where the force was dependent of a motionless charge and the electric field. We were also able to make a relationship for current and the force on the current. This idea is based on the fact that a current consists of many moving charges along a wire. Using the force of magnetism, we are able to apply the force equation to things that involve torque, which is fundamental to electric motors.

Oscilloscope

Purpose:  We take a look at the applications of the oscilloscope. With the oscilloscope, we are able to see how the voltage behaves. We are also about to generate various waves and interpret them

The Cathode Ray Tube

We get a look at a cathode ray tube before we begin using the oscilloscopes. A beam is shot from the inside of the tube and it is moved by the electric field. The electric field applies a force on the beam which causes it shift accordingly.

The Oscilloscope And Voltage

The image shows what the reading of voltage is prior to any voltage put it. We can see that it is at the center of the screen, which we say is our zero voltage.

 After, a voltage is put into the oscilloscope and this cause a shift on the vertical line which in this cane indicates our voltage.

Professor Mason goes over the kind of noise that we can get that can be found on top of a DC power supply. The power supply causes a shift of the horizontal line  in the vertical direction. The noise is a variation of the voltage on top of the voltage the power supply says it would put out.

Our board displays a before and after of the power reading from the oscilloscope. We show that the beam is projected with a horizontal velocity and shift upward due to a electric field by the plates located on top and on the bottom.

Setting Up The Function Generator With A Speaker

We connect the function generator to a speaker so and mess with the frequencies to see what kind of noises we hear. We also switch the types of wave outputted by the function generator. We found that these switches effect the sound.

Connecting A Function Generator To An Oscilloscope

We now play with the controls and see how they affect the oscilloscope. Altering the oscilloscope, we can see if voltage is constant or whether it alternates.

Measuring The Change In Voltage

For DC power supplies, we see that we get a constant voltage and the magnitude of this voltage is seen on the oscilloscope when the horizontal line changes position.

Changing The Frequency Signal Of Two Clean Power Supplies

We connect the oscilloscope to two clean power supplies. These supplies create a nice picture when we tinker with the frequency. The shape on the oscilloscope becomes dependent on the two frequencies of the horizontal and vertical axis. 

Summary Of The Oscilloscope

Mystery Box

The image shows some of data collected from the mystery box. Using this data, we interpret what each color does.

Conclusion:  We find that the oscilloscope does a great job in determining the behavior of voltage on a power supply. Using the visual representations on the oscilloscope, we are able to make conclusions on whether a power supply is a DC or AC supply. We are also able to determine whether a DC power supply truly outputs what it says by checking on the oscilloscope for noise.

Charging And Discharging Capacitors

Purpose:  We attempt to find whether capacitors achieve the potential of the power supply instantaneously or if it takes some amount of time for the capacitor to charge. For this, we utilize Logger Pro to see the behavior of potential as a function of time.

Seeing How Capacitors Charge

To begin, we create a circuit with a power supply, a light bulb, and a capacitor. When all are connected, the light bulb shows no light. This is because the circuit is not completed, as there is a break within the capacitor. This break causes no current to flow. But, what we end up seeing, after time has passed, is that when we disconnect the power supply and only connect the capacitor with the light bulb, the bulb lights up and then begins to dim. This means that the capacitor charged while connected to the power supply which makes sense because we have negative charge gathering at one end of the capacitor and positive at the other end, essentially creating a new power supply. But how fast does a capacitor charge?



We made predictions for the potential of a capacitor and found that we over estimated the potential.

How Fast Does It Charge

When we graph the potential vs. time of the capacitance, we see that the potential increase exponentially.

Charging Rate Of Capacitors

We hook up a new capacitor to a circuit and connect the capacitor to Logger Pro so that we can examine how the potential changes exponentially.

Rate At Which A Capacitor Charges

As we look at how the capacitor charges, we fit the slope of the line with the closest fit equation which turns out to be some variation of the exponential function. We will later interpret what these values actually mean.

Rate At Which A Capacitor Discharges

We observe how a capacitor discharges and find the it goes at an exponential rate as well. The values of the function will, also, be later interpreted.

Deriving The Potential OF a Capacitor As A Function Of Time

We start off by looking at the general equation for capacitance and make it in terms of the potential. We also know that the potential is dependent on the current and the resistance. When we set these two potential equations equal, we solve for the charge. We know that current can be written as the change in q with respect to time. With a little algebra, we set up two integrals and solve for q. We get a definition for the charge of a capacitor with respect to time. Since the charge is proportional to the potential, we can rewrite this equation by replacing the charges with potentials. This gives us our function for potential with respect to time. This looks very similar to the fit equation found in Logger Pro.

How Long Does It Take For A Potential To Charge

We are given a circuit with a switch and when the switch is closed, the emf charges the capacitor. With the given values, we are able to solve for the time that it takes to charge the capacitor. This just involves using our derived formula and plugging in the values.

We take a look at the same problem, but we look at how long the capacitor takes to reach a charge of an electron. This just requires us to alter the potential equation so that it outputs a charge value.

Conclusion:  We find that capacitors take some time to attain potential as well as charge. We found that this time is dependent on an exponential function. As time passes, the capacitor charges quicker and quicker. The same can be said about discharging. There are slight differences between the equations for charge and discharge but the idea is the this occurs exponentially. When a capacitor is connected to a power supply, it charges, and we can then disconnect the power supply and use the capacitor as a new power supply. The only difference is that the power decreases.

Introduction of Capacitance

Purpose:  We begin to investigate what capacitance is and how it is measured. We also go over some of the methods for finding the total capacitance of a number of capacitors, similar to how we found the equivalent resistance.

Quiz Problem

We begin by going over the quiz. The quiz tested our understand of using Kirchhoff's Laws. We had to create two loops in the circuit and write and equation depicting how the potential drops as we go through the loop. This drop should equal to zero. We, then, utilize the relationship between the currents and these three equations, we are able to find the values for the current at different positions. Once we have the current, we are able to measure potential and this allows us to measure how much power is generated by the circuit.

The Inside Of A Capacitor

Professor Mason takes apart a capacitor and we see that there are two conducting plates separated by some material called a dielectric. What the dielectric does is enhance the capacitance of the capacitor by altering the permittivity.  This is important because the capacitance is proportional to the permittivity. It is also proportional to the area of the plates and inversely proportional to the separation distance.

Finding The Capacitance

We decide to solve for the size of the plates needed in order to have a capacitance of one farad and a separation distance of 1 mm in a vacuum space. We found that we need a square sheet of length 3.55 miles. This seem outrageous. To compensate for the area of the sheet, we can put a dielectric between the sheets. This allows us to use a reasonable size sheet for the same amount of capacitance. This demonstrates the importance of dielectrics in capacitors.

Making A Homemade Capacitor

We begin a hands-on experiment by creating our own capacitors using two sheet of aluminum foil.

We use our lab manual to separate the aluminum. This means that the paper acts as a dielectric. The capacitance is then measured at several different separation distances.

The image shows how we placed the aluminum in the lab manual. WE made sure to stick in deep in the manual to prevent the two foils from touching. If they touch, no capacitance is created. We connect the foil to the multimeter to measure its capacitance.



We then created a chart that signified how the capacitance changes as the distance changes. This created an inverse graph that says, as the separation distance increases, the capacitance approaches zero. As the separation decreases, the capacitance approaches an infinite value. This proves the idea the capacitance is inversely proportional to the separation distance.



Our board shows some of the calculations we had to make in order to make the chart used in the previous picture.

Finding Equivalent Capacitance

Like we did with the resistors, we began to see how the total capacitance is found by orienting the capacitors in parallel and in series. We used the multimeter to find the total capacitance and found that the parallel orientation allows us to just add the capacitors to find the total capacitance. If that is the case, we see that this is opposite of the resistor, so we make a reasonable guess that the series orientation is found using inverse sum. This turns out to be true in the end.

We practice finding the equivalent capacitance of a random oriented layout of capacitance and, again, we must look at piece by piece until everything is simplified and we have one value for all of the capacitors.

An Exploding Capacitor

Professor Mason shows us what happens when we put too much potential in a capacitor. The capacitor ends up blowing up. The reason this occurs is because the space within the plates become conductive by a large electrical field. The electric field rips electrons apart causing the space to become conductive and this causes a short circuit, creating a spark.

Conclusion:  We found that Kirchhoff's Laws prove very useful when evaluating a circuit. We also found that the capacitance is proportional to the area and the permittivity and inversely proportional to the separation distance. The permittivity proves to be very useful because it allows us to make large capacitors without using miles of material. We, also, found the technique for find the equivalent capacitance. This is useful because we can configure capacitors in order to achieve the desired capacitance.