000 Induction ENG rev3 20160901 - Yonsei...

General Physics Lab (International Campus) Department of PHYSICS YONSEI University

Lab Manual

Electromagnetic InductionVer.20160901

Lab Office (Int’l Campus)

Room 301, Building 301 (Libertas Hall B), Yonsei University 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA (☏ +82 32 749 3430) / 16

[International Campus Lab]

Electromagnetic Induction

Verify Faraday’s law of induction by observing the current induced in a coil by a changing magnetic flux.

Understand how transformers work.

1. Magnetic Field Lines and Magnetic Flux

A magnetic field line is an imaginary line or curve drawn

through a region of space so that its tangent at any point is in

the direction of the magnetic field vector at that point, as

shown in Fig. 1 and 2. Where adjacent field lines are close

together, the field magnitude is large.

Fig. 1 The magnetic field lines of a permanent magnet. Note that the field lines pass through the interior of the magnet.

The magnetic field lines of a permanent magnet are shown

in Fig. 1. Magnetic field lines point away from N pole and

toward S pole. They also pass through the interior of the

magnet.

Unlike electric field lines, magnetic field lines do not point in

the direction of the force on charge. The force on a moving

charged particle is always perpendicular to the magnetic field,

and hence to the magnetic field line that passes through the

particle’s position.

Fig. 2 Magnetic field lines produced by some common source of magnetic field.

Objective

Theory

----------------------------- Reference --------------------------

Young & Freedman, University Physics (14th ed.), Pearson, 2016

27.3 Magnetic Field Lines and Magnetic Flux (p.911~914)

29.1 Induction Experiments (p.980~981)

29.2 Faraday’s Law (p.981~988)

29.3 Lenz’s Law (p.989~990)

31.6 Transformers (p.1062~1065)

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Lab Manual




We can divide any surface into elements of area as

shown in Fig. 3a. For each element we determine , the

component of normal to the surface at the position of that

element. From the figure, cos . In general, this com-

ponent varies from point to point on the surface. We define

the magnetic flux Φ through this area as

Φ ∙ cos (1)

The total magnetic flux through the surface is the sum of the

contributions from the individual area elements

Φ ∙ cos (2)

Magnetic flux is a scalar quantity. If is uniform over a

plane surface with total area , then and are the

same at all points on the surface, and

Φ ∙ cos (3)

The SI unit of Φ is called the weber (1Wb 1T ⋅ m ).

Fig. 3 (a) Calculating the magnetic flux through an area ele-ment. (b-d) Calculating the flux of a uniform magnetic field through a flat area.

2. Faraday’s law of induction

After Oersted found that a compass needle was deflected by

a current-carrying wire, Faraday began to think about the

experiment in a different way: if electricity induces magnetism,

then could magnetism induce electricity also? In 1831, using

an iron ring wound two insulated coils, he found that upon

passing a current through one coil a momentary current was

induced in the other coil. In subsequent experiments, he

found that when he moved a magnet through a loop of wire

an electric current flowed in that wire.

Fig. 4 A diagram of Faraday’s iron ring-coil apparatus and the first transformer made by Faraday on August 1831.

Fig. 5 shows several examples of electromagnetic induction.

When the nearby magnet is stationary, the meter shows no

current. But when we move the magnet either toward or away

from the coil, the meter shows current in the circuit, but only

while the magnet is moving. We call this an induced current,

and the corresponding emf required to cause this current is

called an induced emf.

Fig. 5 Demonstrating the phenomenon of induced current.


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We connect a coil to a galvanometer and then place the coil

between the poles of an electromagnet whose magnetic field

we can vary, as Fig. 6. Here’s what we observe:

① When there is no current in the electromagnet, so that

0, the galvanometer shows no current.

② When the electromagnet is turned on, there is a momen-

tary current through the meter as increases.

③ When levels off at a steady value, the current drops to

zero, no matter how large is.

④ If we squeeze it so as to decrease the cross-sectional

area of the coil, the meter detects current only during the

deformation. If we increase the area to return the coil to its

original shape, there is current in the opposite direction.

⑤ If we rotate the coil a few degrees about a horizontal axis,

the meter detects current during the rotation, in the same

direction as when we decreased the area. When we rotate

the coil back, there is a current in the opposite direction.

⑥ If we jerk the coil out of the magnetic field, there is a cur-

rent during the motion, in the same direction as when we

decreased the area.

⑦ If we decrease the number of turns in the coil by unwind-

ing one or more turns, there is a current during the unwind-

ing, in the same direction as when we decreased the area.

If we wind more turns onto the coil, there is a current in the

opposite direction during the winding.

⑧ When the magnet is turned off, there is a momentary

current in the direction opposite to the current when it was

turned on.

⑨ The faster we carry out any of these changes, the great-

er the current.

Fig. 6 A coil in a magnetic field. When the field is constant and the shape, location, and orientation of the coil do not change, no current is induced in the coil. A current is induced when any of these factors change.

The common element in all these experiments is changing

magnetic flux through the coil. In each case the flux changes

either because the magnetic field changes with time or be-

cause the coil in moving through a nonuniform magnetic field.

In all of situations the induced emf is proportional to the rate

of change of magnetic flux Φ through the coil.

Faraday’s law of induction states that the induced emf in a

closed loop equals the negative of the time rate of change of

magnetic flux through the loop.

In symbols, Faraday’s law is

Φ

(4)

If we have a coil with identical turns, and if the flux varies

at the same rate through each turn, the total rate of change

through all the turns in times as large as for a single turn.

If Φ is the flux through each turn, the total emf in a coil with

turns is

Φ

(5)

Fig. 7 The magnetic flux is becoming (a) more positive, (b) less positive, (c) more negative, and (d) less negative. Therefore Φ is increasing in (a) and (d) and decreas-ing in (b) and (c). In (a) and (d) the emfs are negative, and in (b) and (c) the emfs are positive.


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3. Transformer

A transformer is an electrical device that transfers energy

between two or more circuits through electromagnetic induc-

tion, and commonly used to increase or decrease the voltage

of alternating current in electric power applications.

Figure 8 shows an idealized transformer. The key compo-

nents of the transformer are two coils electrically insulated

from each other but wound on the same core. The core is

typically made a material with a very large relative permeabil-

ity. This keeps the magnetic field lines due to a current in one

winding almost completely within the core. The winding to

which power is supplied is called the primary; the winding

from which power is delivered is called secondary.

The ac source causes an alternating current in the primary,

which sets up an alternating flux in the core; this induces an

emf in each winding, in accordance with Faraday’s law. The

induced emf in the secondary gives rise to an alternating cur-

rent in the secondary, and this delivers energy to the device

to which the secondary is connected.

We assume that all the magnetic field lines are confined to

the iron core, so at any instant the magnetic flux Φ is the

same in each turn of the primary and secondary windings.

The primary winding has turns and the secondary wind-

ing has turns. When the magnetic flux changes because

of changing currents in the two coils, the resulting induced

emfs are

Φ

andΦ

(6)

The flux per turn Φ is same in both the primary and the

secondary, so equations (6) show that the induced emf per

turn in the same in each. The ratio of the secondary emf

to the primary emf is therefore equal at any instant to the

ratio of secondary to primary turns:

(7)

If we neglect the resistance of windings, the induced emfs

and are equal to the terminal voltages across the pri-

mary and the secondary, respectively; hence

(8)

where and are either the amplitudes or the rms values

of the terminal voltages.

By choosing the appropriate turns ratio ⁄ , we may ob-

tain any desired secondary voltage from a given primary volt-

age. If , as in Fig. 8, then and we have a

step-up transformer; if , then and we have a

step-down transformer.

Fig. 8 Schematic diagram of an idealized step-up transformer.


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1. List

Item(s) Qty. Description

PC / Capstone software

1 Records, displays and analyzes data measured by var-

ious sensors.

Interface

1

Data acquisition interface designed for use with various

sensors, including power supplies which provide up to

15 watts of power.

Photogate

(Post and Cable included)

1 set Measures high-speed or short-duration events.

Voltage Sensor

1 Measures terminal voltages.

Patch Cords

(with banana plugs)

2 Carry electric current.

Transformer (Demountable)

1 set

Demonstrates the principles of transformers.

* Laminated U-Core & I-Core, Clamping Bolt,

Coils 200, 400 2 , 800, 1600, 3200

Bar Magnet

1 Produces a magnetic field.

Tube

1 Guides magnets to pass through coils.

Tube Clamp

1 Provides stable support for a guide tube and coils.

Equipment


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Items Qty. Description

A-shaped Base

1 Provides stable support for experiment set-ups.

Support Rod

(600mm)


Multiclamp


Cushioned Basket

1 Absorbs shock on impact.

2. Details

(1) Photogate

The photogate sensor is an optical timing device used for

very precise measurements of high-speed or short-duration

events. It consists of a light source (infrared LED) and a light

detector (photodiode). When an object moves through and

blocks the infrared beam between the source and the detec-

tor, a signal is produced which can be detected by the inter-

face.

When the infrared beam is blocked, the output signal of the

photogate becomes ‘0’ and the LED lamp on the photogate

goes on. When the beam is not blocked, the output signal

becomes ‘1’ and the LED is off. This transition of signal can

be used to calculate quantities such as the period of a pen-

dulum, the velocity of an object, etc.

(2) Voltage Sensor

The voltage sensor is a bipolar sensor

which is used to measure the terminal

voltage in DC or AC circuits.

(3) Demountable Transformer

The demountable transformer is designed for demonstration

the principles of step-up and step-down transformers and

electromagnetic induction. The number of turns and the di-

rection of the windings are indicated on the coil assembly.


Lab Manual




Experiment 1: Electromagnetic Induction I

(1) Set up your equipment.

Mount the coil of 1600 on the tube clamp.

Position the photogate and the tube as below so that the

magnet can block infrared beam of the photogate when the

magnet passes through the transparent plastic tube.

The number of turns and the direction of the windings are

indicated on the coil assembly.

(2) Run Capstone software.

(2-1) Add sensors.

Click the ports which you plugged the sensors into and se-

lect [Photogate] or [Voltage Sensor] from the list.

Procedure

Caution

The bar magnet will be dropped through the tube. Place

the cushioned basket under the tube. Make sure the

magnet does not strike the table without cushion, or it

may break.


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(2-2) Create a timer for the photogate.

Create a timer to configure automatic recording conditions.

(The photogate works as an optical switch which generates

an electrical signal when the magnet passes through it.)

Click [Timer Setup] in the [Tools] palette and follow the steps

below to create a timer.

Check [State] at step ④. [State] outputs the value of state

of the photogate. The photogate generates ‘1’ while it is

blocked, and ‘0’ while open.

Skip steps ⑤ to ⑥ and finish the timer setup.

(2-3) Configure automatic recording conditions.

We will start recording data automatically when a certain

condition is achieved. Click [Recording Conditions] in the

[Controls] palette.

Measurement will be started automatically at the very mo-

ment the photogate is blocked (the state of the photogate

becomes ‘1’). Set the parameters of [Start Condition] as be-

low.

[Condition Type] : Measurement Based

[Data Source] : State()

[Condition] : Is Above

[Value] : 0.5

Measurement will be continued only for 0.5 seconds. Set the

parameters of [Stop Condition] as below. (You can change

the record time if required.)

[Condition Type] : Time Based

[Record Time] : 0.500 s


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(2-4) Confirm the automatic recording configuration.

You can see the [Record] button at the beginning.

If you click [Record], the program will waits until the start

condition is achieved. ([Record] toggles to [Stop] and record-

ing status display under the timer indicates [Waiting].) Even if

the timer is ticking, no data is recorded.

If you block the photogate (start condition) using your finger,

data recording will start automatically. The recording status

display indicates [Recording].

Data recording will end automatically after 0.5 seconds (stop

condition).

(2-5) Adjust the sample rate of measurements.

Select [10.00kHz] for voltage sensor in the [Controls] palette.

(2-6) Create a graph display.

Click and drag the [Graph] icon from the [Displays] palette

into the workbook page. Select [Time(s)] for the -axis and

[Voltage(V)] of the voltage sensor for the -axis.

(3) Begin recording measurements.

When the magnet is passed through the coil, there is a

changing magnetic flux, which induces an emf in the coil. We

use the voltage sensor to measure the voltage induced in the

coil as the bar magnet moves through the coil.

Click [Record], and drop the magnet through the tube. Make

sure the magnet blocks the infrared beam of the photogate

when it passes through the photogate.


Lab Manual




(4) Analyze your graph.

[Scale axes …] rescales the graph automatically.

You can also scale or pan the graph manually.

[Select range …] selects the data range of interest.

[Display area …] measures the area between the curve and

-axis.

You can see more precise value of the area by converting

the unit of measurement.

[Show coordinates …] shows the coordinate of each data

point in the plot.


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[…viewing of multiple runs | Select …] or [▼] activates plot-

ting multiple runs together, or changes visible run.

You can change the name of each run as follows.

(5) Analyze your results.

Measure the areas of each peak, and the values of maxi-

mum and minimum points of the curve.

Suppose the magnetic field lines of the magnet have perfect

symmetry and the magnet passes a single turn of wire loop.

Answer the following questions.

Φ

(4)

Q What is the physical meaning of the ‘area’ under the

curve?

A

Q Where is the position of the magnet when the sign of

voltage changes? Explain why.

A

Q Compare the areas of each peak and explain the reason

of the result.

A

Q

What is the physical meaning of the maximum and mini-

mum values of the curve? Compare the absolute values of

them. If there is any difference between them, explain why.

A


Lab Manual




Note

We can create a graph of area under the curve as a

function of time, as follows.

① Click [Calculator] in the [Tools] palette, and define

the equation as below. (Refer to the instructions of the

program for defining functions.)

② Create a graph display and add a new plot area with

shared -axis.

③ Choose [Time(s)] for -axis, and [Voltage(V)] and [Φ

(user defined data)] for -axes.

The lower (green) graph is a qualitative depiction of

magnetic flux as a function of time. We can understand

the relation between the change of magnetic flux and the

induced emf from the graphs. Refer to the Faraday’s law

of induction.


Lab Manual




Experiment 2: Electromagnetic Induction II

Repeat the experiment with the magnet reversed.

- Direction of poles : reversed

- Turns of coil : same as 1st experiment ( 1600)

- Drop height : same as 1st experiment

Q How does the graph change? Explain the reason of the

result.

A

Experiment 3: Electromagnetic Induction III

Repeat the experiment with varying the dropping height of

the magnet.

- Direction of poles : same as 1st experiment

- Turns of coil : same as 1st experiment ( 1600)

- Drop height : higher than 1st experiment

Q

How does the graph change if you drop the magnet from

a larger height? Is the peak of the graph higher or smaller;

wider or narrower? Explain the reason of the result.

A

Experiment 4: Electromagnetic Induction IV

Repeat the experiment using different turns of coils.

- Direction of poles : same as 1st experiment

- Turns of coils : 200, 400, 800, 1600, 3200

- Drop height : same as 1st experiment

Q Express the relation between the turns of coil and the

induced emf. Explain the reason of the result.

A

Experiment 5. Transformer

(1) Build a transformer and connect the cables.

Primary: 400

Secondary: 200

Caution

To avoid scratching or stabbing the coils, handle them

with care and keep them in the storage box when not in

use.


Lab Manual




(2) Set up the Capstone program.

(2-1) Add sensors.

Click the ports which you plugged the Voltage Sensor or

patch cords into and select [Voltage Sensor] or [Output Volt-

age Current Sensor] from the list.

(2-2) Configure the signal generator.

[Signal Generator] [850 Output 1]

[Waveform] : Sine

[Frequency] : 50Hz

[Amplitude] : 1V

[Auto] (starts or stops the generator automatically.)

(2-3) Create a scope.

Click and drag the [Scope] icon from the [Displays] palette

into the workbook page.

Add independent -axis on the right side of the graph by

clicking [Add new -axis…].

-axis: Time(s)

-axis(left): Output Voltage, Ch 01 (V)

(signal generator output, or primary input)

-axis(right): Voltage, Ch A (V)

(voltage sensor, or secondary output)

(2-4) Select [Fast Monitor Mode] in the controls palette.

[Fast Monitor Mode] displays data without recording. Check

that [Recode] button is changed to [Monitor] button.


Lab Manual




(3) Start monitoring data.

(3-1) Click [Monitor] in the controls palette.

(3-2) Click [Activate … trigger] in the toolbar to horizontally

align repetitions of the signal.

(3-3) Scale the display

(3-4) Find the axis of each trace.

Color in legend matches plot color.

[Vo]: Output Voltage, Ch 01 (V) (left -axis) (primary input)

[V]: Voltage, Ch A (right -axis) (secondary output)

(3-5) Measure the amplitudes.

Click [Show data coordinates…] and read off the peak of

each trace.

(4) Analyze your results.

Compare the ratio of to with the ratio of to

and verify the equation (8).

(8)

(5) Repeat your experiment.

Repeat measurement for other combinations of coils.

Primary: 400

Secondary: 200, 400, 800, 1600, 3200

⁄ ⁄

1

400

200 0.5

1V

2 400 1

3 800 2

4 1600 4

5 3200 8


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Your TA will inform you of the guidelines for writing the laboratory report during the lecture.

Please put your equipment in order as shown below.

□ Delete your data files and empty the trash can from the lab computer.

□ Turn off the Computer and the Interface.

□ Do not disassemble your equipment.

□ When you unplug the Photogate Cable from the photogate, pull on its connector, not on the cable itself.

This connector has a locking tab. Press in on the locking tab before you unplug the cable.

□ Keep the Magnet in the cushioned basket.

□ Keep the Transformer Set in the storage box.

Result & Discussion

End of Lab Checklist

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