# Eddy Currents And Braking Forces Engineering Essay

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An Eddy Current is a closed loop current that flows in a conductor. They are created when a conductor's magnetic field is exposed to change, usually when the conductor comes in contact with another magnetic field or when a stationary object enters the conductor's magnetic field. These currents circulate and create electromagnets with magnetic fields that will oppose the change in the external magnetic field. In other words, the eddy current will be created in the opposite direction of the field's movement.

Electromagnetic braking in trains: http://www.deschamps-web.com/site/eb/frein/partie3/partie60.jpg

Eddy Currents are used for electromagnetic braking in trains and roller coasters as they both travel at a very high level of inertia thus making it difficult for them to safely break or halt motion. In a train, electromagnets placed close to the metal rails induce eddy currents which then produce magnetic fields within the rails. The interaction between the magnetic fields opposes the forward motion of the electromagnets and the train which results in the deceleration of the train because the strength of the induced eddy currents is directly proportional to the speed of the train thus the braking force is reduced as the train slows down. In a roller coaster, a copper plate is attached to the ride carriage. As the ride passes between permanent strong magnets attached near the bottom of the track, eddy currents are created as well as opposite magnetic poles in the copper plate and magnets. The collective effect of interaction between the permanent magnets and copper plate slows the ride; because like the train the strength of the eddy currents within the plate is directly proportional to the speed of the plate moving between the magnetic poles thus as the ride slows the braking force is reduced.

Advantage of Magnetic Braking Mechanisms:

Virtually fail safe as it relies on the basic properties of magnetism and is not affected by various elements such as rain like friction brakes.

No mechanical wear and tear, therefore there is no need to replace

Produces a precise breaking force

Eddy currents have an unfavorable effect in transformers because transformers work by running a current at a specific voltage through one current loop which in turn creates a magnetic field. However when eddy currents are generated in the transformer's metal core, the eddy currents cause the metal core to lose power and energy. This primary investigation will highlight the effect eddy currents have on the braking forces of objects, which as established above is very important.

## Aim:

To determine if the type of material and the thickness of material has an effect on the braking force of an object. Through the use of electromagnets, the experiment will also determine if eddy currents have a direct impact on the braking force of an object.

## Hypothesis:

Newton's second law states that the force applied to an object produces a proportional acceleration. From the experiment, the braking force created by eddy currents will have a direct impact on the deceleration of a pendulum in motion. As copper has a lower resistivity, it should have the greatest braking force as the eddy currents will have a greater impact on the motion of the copper pendulum. Brass has a high resistivity; therefore it should have a much lower braking force caused by the eddy currents.

The thicker the conductive plate, the greater the braking force because resistivity decreases as thickness increases thus the braking force created by the eddy currents will be greater. The more conductive a plate is, the greater the eddy currents that will be produced as there is less resistivity. Also, the greater the magnetic flux density and area of the conductive plate results in a greater magnetic flux. Therefore the thicker the conductive plate the greater the magnetic field that will be created, thus resulting is a greater braking force.

## Variables:

Independent: Thickness of material and Type of material

Dependent: Braking Force

## Equipment:

Connecting wires

Video Camera

Compass

Supporting Frame

Plastic tubing

Microammeter (to test current)

2 Electromagnets

1 Transformer (power pack)

2 Copper pendulums, varied thickness

2 Aluminium pendulums, varied thickness

2 Brass pendulums, varied thickness

## Safety:

Ensure transformer (power pack) is turned off when circuit is being connected

## Method:

Measure the thickness of each pendulum using a screw gage, then weigh the pendulum. Record the thickness and weight of each pendulum.

Fig 1.1 - Apparatus set-up

Position the supporting frame and plastic tubing on the axel of where the pendulum will hang (so that the pendulum does not move back and forth) and connect electromagnets in series using the power pack, connecting wires and electromagnets. (Fig. 1.1) Note that electromagnets must have opposite poles in order for magnetic force to be present. Test the poles by using a compass.

Voltage: 8 V

Current: 0.1 mA

Attach pendulum 1 to supporting frame.

Turn off magnet and pull pendulum up to specific height.

Record the motion of the pendulum upon release using the video camera.

Release the pendulum. Observe until the pendulum comes to a stationary position. Stop video recording.

Repeat process 5-7 this time with the electromagnet on.

Attach the next pendulum to supporting frame. Repeat steps 5-9 until all pendulums have been used in the experiment (2 copper, 2 aluminium, 2 brass - all varied thickness)

Input each video into tracker. Using tracker, find the initial velocity of each pendulum swing. Note: The final velocity = 0

Calculate acceleration and Braking Force using velocity results obtained from tracker.

To obtain the results from the experiment, tracker had to be used to find points needed to calculate the initial velocity. To find the initial velocity, we used the formula m=|y2-y1 | | x2-x1 |

To find the acceleration of the pendulum: a = - u _

## 0.033s x (# of frames v - u)

0.033 is the rate at which the video camera captures image

To find the Braking Force of the pendulum: F = m a

## Patterns, Trends and Discrepancies:

Patterns and Trends:

From the experiment each pendulum was tested with the electromagnets and without the electromagnets. From the results a defining pattern emerged the braking force will always be greater when the electromagnets are turned on than when they were turned off. This clearly shows the effect eddy currents have on a conductor. The eddy currents are created when the conductor's (metal pendulum) magnetic field is exposed to change. In this case, when the conductor comes in contact with the magnetic field of the electromagnets, these currents circulate in the opposite direction of the conductor's movement which then results in a greater breaking force.

Braking force is dependent on the thickness of the material.

From the results, it is clear that the thicker the material the greater the braking force. This is due to the fact that resistivity decreases with increasing thickness. For example in the graph, copper 0.55mm has a higher braking force than copper 0.15mm.

REASON: The resistance of an object depends on the length of the wire, the thickness of the object, and the resistivity of the material. Resistance increases with length, decreases with area and increases with resistivity. Below is the equation for determining the resistance in an object:

It can be rearranged to find the resistivity of an object: resistivity (p) = resistance (R) Ã- area (A) / length (l)

As resistivity depends on the resistance of an object multiplied by the area of the object and divided by the length. When the pendulum is of the same material and the same size/length then the area(thickness) of the object determines the differences in braking force.

Braking force increases when the material of the pendulum has a low resistivity.

## Resistivity

Copper

1.7 x 10-8

Aluminium

2.82 x 10-8

Brass

3.9 x 10-8

http://en.wikipedia.org/wiki/Resistivity

From the results, it is evident that copper has the largest braking force, followed by aluminium then brass. We can assume that this is due to the differences in resistivity. Copper has the lowest resistivity thus the metal does not resist the magnetic field created eddy currents thus it decelerates faster than the other two materials.

Discrepancies:

0.81 Brass results however do not adhere to the above trend. The braking force of the pendulum without the magnet is greater than the braking force of the pendulum with the magnet. This anomaly is probably due to an error from using tracker as video is recorded at 0.033 seconds and when the video is inputted into tracker, certain frames can be blurred as the pendulum is in motion thus making it difficult to get an accurate point of mass point and determine the x and y points which enable the calculation of the initial velocity. Thus if the values obtained from tracker are incorrect, then the rest of the calculations will also be affected.

On the graph, it is clear that the lines that represent the various materials do not go through the origin. Theoretically they should pass through the origin because if a pendulum has 0mm thickness then it would have 0 N braking force. Although theoretically without the electromagnets the pendulums should have taken the same amount of time to come to a stop as they are the same shape and size. However as drag (friction) is responsible for bringing the pendulum to a stop, there is no uniform level of friction. There is friction on the pendulum mechanism and therefore is not possible to have a uniform level of friction it will always be different on each pendulum. In order to have overcome this, the pendulum mechanism of which the pendulum swings on should have been filed down so that it would be smooth. This would reduce the friction, resulting in the pendulum swinging for a longer amount of time.

## Strengths of approach:

Using thickness as a variable

Using the supporting frame during the experiment

Using type of material as a variable

Control experiment (pendulum motion without electromagnet) for each different pendulum

## Weaknesses of approach:

Using tracker to track the motion of the pendulum and determine the initial velocity from video footage because as stated above, the video camera captures footage at 0.033 seconds which when inputted into tracker presents some difficulty as in certain frames the pendulum is a blur and in order to gain the points of deceleration as the pendulum swings some guesswork is involved as to where the edge of the pendulum is.

In the experiment, we did not do any repeats of each pendulum. This was a mistake as we could not check if the results obtained were in fact correct or whether it was just by accident and in fact not absolutely correct. If we had done repeat tests of each pendulum with and without magnets we could then take the average of each result which would make our results more accurate and lower the percentage error.

## Changes to the original plan:

Originally we planned to use a magnet as a pendulum hung from a retort stand over a sheet of copper/aluminium/brass.

However we decided that it would be difficult using a permanent magnet as the pendulum as we could not measure the strength of the magnet without significant error. Therefore we decided to use different materials for the pendulum such as copper/aluminium/brass instead of a sheet at the bottom. We decided that using electromagnets would also be better as we could select the voltage (8V) and measure the current with an ammeter.

Also instead of using a retort stand we decided to use a supporting frame as it would be more stable and we could release the pendulum at the same height each time without worrying about whether we released it at the same point.

## Potential Sources of Error:

Measuring the thickness of each pendulum using a screw gage

Measuring the mass of each pendulum

Using the video camera and tracker to track the motion of the pendulum and the time it took for the pendulum to stop

## Conclusion:

The analysis of the results obtained support my hypothesis because from the results we established that the thickness of the material has a direct effect on the braking force of the object; braking force increases when the material of the pendulum has a low resistivity and that the braking force of the pendulum is greater when electromagnets are used.

With thickness as the independent variable and the braking force as the dependent variable, through the results, graph and analysis it is evident that when the thickness increases, the resistivity decreases which then results in the braking force increasing.

With type of material as the independent variable and the braking force as the dependent variable, through the results, graph and analysis it is evident that the type of material has a direct impact on the braking force as each material has a different resistivity.

If this experiment were to be done again, I would use a photo gate sensor to obtain the initial velocity instead of using the video camera and tracker as with the camera we have to take into account that it takes an image every 0.033 seconds which lowers the accuracy. Also using tracker was quite difficult as the frames were at times not very clear due to the 0.033s difference of each frame therefore it was hard to identify the point of mass points accurately and was somewhat subjective. Most important of all I would test each pendulum a number of times in order to ensure accuracy. Other than that I think the experiment worked fairly well.

## Outline Michael Faraday's discovery of the generation of an electric current by a moving magnet.

Michael Faraday was an English chemist and physicist best known for his pioneering experiments in electricity and magnetism. In 1785, Charles Coulomb demonstrated how electric charges repel one another. In 1820 Hans Christian Oersted and Andre Marie Ampere discovered that an electric current produces a magnetic field.

This led Faraday to believe that since an electric current could create a magnetic field, a magnetic field in turn should be able to produce an electric current. This was based on his ideas about the conservation of energy. In 1831 Faraday demonstrated this through an experiment:

Attaching two wires through a sliding mechanism to contact a copper disc that is rotating, the disc is located between the poles of a horseshoe magnet. This set-up was the equivalent of shifting a magnetic field close to an electric circuit which in turn induced a continuous direct current.

Faraday explained that the moving disk induced the electric current because it cut a series of magnetic force lines that were emanating from the magnetic field. An external circuit for the current to flow through is created through the use of the connecting wires. This experiment was the invention of the first electric generator.

## Describe the concept of "magnetic flux" and how it relates to magnetic flux density (B) and surface area (A).

The concept of "magnetic flux" is a measure of the quantity of magnetism, taking into account the strength of the magnetic field. Magnetic flux {measured in Webers (Wb)} is the amount of magnetic field that is flowing through a certain area (A). This can be represented by the total number of magnetic flux lines that pass through the area. This relates to magnetic flux density (B) {measured in Webers per sq. metre (Wb m-2)} because the stronger the magnetic field in a specific point the higher the magnetic flux density (B) at that specific point which means there are more magnetic flux lines that are passing through that area.

To calculate the magnetic flux (total amount of perpendicular magnetic field passing through an area or a surface (A)):

Flux = Flux Density x Area

= B x A

## Outline Lenz's Law and account for Lenz's Law in terms of conservation of energy.

Lenz discovered a way to find the direction of the induced electric currents that were predicted by Faraday's law which states that an electric current that is induced by a changing magnetic field will in turn induce its own magnetic field. Lenz's law states that whenever there is an induced electromotive force (emf) within a conductor, it will always be in a direction that the current created will oppose the change which causes the induced emf. This law is a result of the Law of Conservation of Energy which states that in the changing from one form to another, energy is always conserved.

For example: A current is produced from the insertion of a magnet into a coil of wire that is connected to a circuit with a micrometer. The moving magnet creates an electric current in the wire which then creates its own magnetic field. In accordance with Lenz's law, the created magnetic field must oppose the moving magnet (the cause of the magnetic field). Thus the magnetic field will be in the direction that will try to stop the moving magnet. Hence it adheres to the Law of Conservation of Energy. If the current did not oppose the moving magnet, the created magnetic field would then increase the magnet's velocity which would then increase its kinetic energy which bypasses the Law of Conservation of Energy.

## Outline how the magnetic induction is used in cook-tops in electric ranges.

Magnetic induction does not involve generating heat which is then transferred to the cook-top. Instead it makes the cook-top itself the heat generator to cook the food. Magnetic Induction is used in cook-tops in electric ranges through the use of electricity to produce a magnetic field that sends currents into iron atoms that react by movement which causes friction and heat in a metal vessel.

## How Induction Cooking Works:

Electricity powers a coil (represented by the red lines) that in turn produces an alternating current of a high frequency is passed through the coil creating a fluctuating electromagnetic field (represented by the orange lines).

That field penetrates the metal of the ferromagnetic material cooking vessel and sets up a circulating electric current, in other words an eddy current, which generates heat.

The heat generated in the cook-top is transferred to the cook- tops contents.

Nothing outside the cook-top is affected as the eddy currents fields are kept within the cook-top as it is an electrical insulator.

How induction cooking works diagram: http://theinductionsite.com/how-induction-works.shtml

## Discuss the need for step-up and step-down transformers in the transfer of electrical energy from a power station to its point of use.

A step-up transformer provides an output voltage that is greater than the input voltage.

A step-down transformer provides an output voltage that is less than the input voltage.

In the transfer of electrical energy from a power station to its point of use step-up and step-down transformers are needed because at power stations they need a step-up transformer to increase the voltage and reduce the current for long distance transmission because from the power station the electrical energy produced must be transported to the various substations and in towns. At the substations and towns a step-down transformer is used to reduce the transmission line voltage so that it can be used for both domestic and industrial use.