Wingfield 182B 196L Lab 8 PDF

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE

Lab 8: Faraday’s Law and Inductance San Diego State University Department of Physics Physics 182B/196L Name:

Amaya Wingfield

Date:

11/3/2020

Score:

Theory: British scientist Michael Faraday did most of his work in the 1820’s and 1830’s. During this period of time, he discovered almost all of the basic principles of electro-magnetism. His greatest discovery was the production of an electric field by a changing magnetic field. This is referred to as Faraday’s Law of Magnetic Induction, or Faraday’s Law. Mathematically, Faraday’s Law can be written: V = N Δɸ/Δt Here, V is the induced voltage, Δɸ is the change in the lines of magnetic flux enclosed by the coil, N is the number of turns in the coil, and Δt is the time over which the change in magnetic flux occurs. Note that V is proportional to both the number of turns in the coil and the change in magnetic flux. V is inversely proportional to the time taken for the magnetic flux to change. The deltas in Faraday’s Law are important. Δɸ tells us that a voltage is only induced in a coil if the magnetic field is changing. 1/Δt tells us that greater voltages are induced if the magnetic field changes quickly. American physicist Joseph Henry competed with Michael Faraday in the discovery of new electromagnetic phenomena. Joseph Henry built upon Faraday’s work and discovered that, as a result of Faraday’s Law, coils resist changes in current flow. Henry introduced the concept of inductance and modified Faraday’s Law: V = L ΔI/Δt Here, L is the inductance and ΔI is the change in current. L is measured in units of Henrys (H). Henry discovered that the magnetic field of one coil could interact with a nearby coil, changing

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE the inductance of either coil. This effect is called mutual inductance, and is given the symbol M. The amount of mutual inductance depends on the spacing and orientation of each coil. Faraday’s Law: Image 8.1 shows a coil connected to the oscilloscope, along with a bar magnet that can be used to induce a voltage in the coil. Image 8.2 shows the coil voltage when there is no movement of the magnet. The horizontal line represents zero volts.

[Image 8.1 – Faraday’s Law Coil Setup]

[Image 8.2 – Magnet Not Moving, Zero Coil Voltage]

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE In order to see the induced voltage when the bar magnet is moved in and out of the coil, the time base is set to 0.1 s/div and the camera shutter speed is set to 1 second. As the magnet moves into and out of the coil, there are changes in magnetic flux and, according to Faraday’s Law, a voltage is induced. Because the motion of the magnet is momentary, the induced voltages appear as pulses. The polarity (whether the voltage is positive or negative with respect to zero volts) of the pulse depends on the orientation of the magnetic field and the direction of motion. Images 8.3 and 8.4 show the induced voltage when the north pole of the bar magnet is moved into and out of the center of the coil.

[Image 8.3 – North Pole Moving Into the Coil]

[Image 8.4 – North Pole Moving Out of the Coil]

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE Images 8.5 and 8.6 show the induced voltage when the south pole of the bar magnet is moved into and out of the center of the coil.

[Image 8.5 – South Pole Moving Into the Coil]

[Image 8.6 – South Pole Moving Out of the Coil]

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE Examine images 8.3 – 8.6 and determine the initial polarity (positive or negative) of the induced voltages: Polarity North Pole Moving In

Positive

North Pole Moving Out

Negative

South Pole Moving In

Negative

South Pole Moving Out

Positive

Image 8.7 shows the induced voltage when the south pole of the bar magnet is moved out of the center of the coil at a rate that is slower than the rate in image 8.6.

[Image 8.7 - South Pole Moving Out of the Coil (Slower)] Compare Images 8.6 and 8.7. Which image is associated with a larger amplitude? Smaller amplitude? Which image is associated with a larger Δt? Smaller Δt? Image Number Larger Amplitude

8.6

Smaller Amplitude

8.7

Larger Δt

8.7

Smaller Δt

8.6

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE

Recalling Faraday’s Law:

V = N Δɸ/Δt

Does Faraday’s Law predict the results of the above comparison and, if so, why? Faraday's law says that emf is always proportional to the change of the magnetic fluid. So when time is increased the voltage will decrease.

The Transformer: A transformer is made by combining two coils. In a transformer, a voltage applied to one coil induces a voltage in the other coil. Image 8.8 shows a pair of identical coils set up as a transformer. The left coil is the primary coil and remains fixed in place. The right coil is the secondary coil and it can be moved. The primary coil is connected to the function generator producing 2 KHz sine waves with an amplitude of 3.0VPP. On the oscilloscope, channel 1, displays the input or primary voltage. Channel 2 displays the output or secondary voltage.

[Image 8.8 – The Transformer] Images 8.9 – 8.12 show the oscilloscope display for different center-to-center coil separations. In images 8.9 – 8.11, the secondary coil is parallel to the primary coil. In image 8.12, the secondary coil is perpendicular to the primary coil. In each of the images, the upper waveform (channel 1) is the 3.0 VPP primary input voltage and the lower waveform (channel 2) is the secondary output voltage. Channel 2 vertical scale factors are indicated in the images and table below.

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE

[Image 8.9 – Parallel Secondary Coil, Separation = 4 cm, Ch2 Scale = 0.5 V/DIV]

[Image 8.10 – Parallel Secondary Coil, Separation = 8 cm, Ch2 Scale = 0.2 V/DIV]

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE

[Image 8.11 – Parallel Secondary Coil, Separation = 12 cm, Ch2 Scale = 0.1 V/DIV]

[Image 8.12 – Perpendicular Secondary Coil, Separation = 12 cm, Ch2 Scale = 0.1 V/DIV]

Examine images 8.9 – 8.12 and determine the secondary voltage for each separation. Calculate the ratio of VSecondary/VPrimary:

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE

Coil

Secondary Coil

Separation

Primary Voltage

# of Div

V/DIV

3 VPP

3

0.5 V/Div

Orientation 4 cm

Parallel

Secondary

Ratio Voltage

VSec/VPri

1.5/3=.5V 3x.5=1.5 V

8 cm

Parallel

3 VPP

3

0.2 V/Div

3x.2=.6V

.6/3=.2V

12 cm

Parallel

3 VPP

3

0.1 V/Div

3x.1=.3V

.3/3=.1

12 cm

Perpendicular

3 VPP

3

0.1 V/Div

3x.1=.3V

.3/3=.1

For the parallel secondary configurations, does the secondary voltage increase or decrease with increasing coil separation? Secondary voltage will decrease because the induction will be less as the coil separates.

Explain what causes the secondary voltage to change as the separation changes: Secondary voltage is linked with separation so as one increases one must decrease to keep the balance.

Explain what causes the difference in secondary voltage for the two 12 cm separation cases: If the separation is lower than the induction it will be high along with the voltages. But, if separation is high than the induction is affected meaning the voltages will be lower.

Mutual Inductance: Because the magnetic field associated with a coil extends beyond the coil itself, it can interact with another nearby coil. This interaction produces mutual induction and is given the symbol M. In the absence of mutual induction, the inductance of a single coil is called the self inductance, symbolized by LSELF. If two identical coils are wired together in series, the total induction is the sum of the mutual induction and two times the self induction:

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE LTOTAL = M + 2LSELF

Image 8.13 shows two identical coils wired in series and connected to a multimeter set to measure inductance:

[Image 8.13 – Measuring Inductance]

Image 8.14 shows the inductance measurement for a single coil (LSELF).

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE [Image 8.14 – The Self Inductance for a Single Coil]

Record this value and the value for 2LSELF in the table: LSELF

2LSELF

16.5 mH

16.5x2= 33 mH

In the next table, total inductance measurements are given for different center-to-center coil separations for two identical coils wired in series. The ‘winding configuration’ refers to whether windings in the second coil have the same or opposite sense of direction with respect to the first coil. For the first 6 measurements, the coils are oriented parallel to each other. The last measurement was made with the second coil oriented perpendicular to the first coil. For each measurement, calculate and record the mutual inductance: M = L TOTAL - 2L SELF Coil

Winding

L TOTAL

2L SELF

M

Separation

Configuration

(mH)

(mH)

(mH)

4 cm

Same

45.0

33

12

4 cm

Opposite

21.0

33

-12

8 cm

Same

39.0

33

6

8 cm

Opposite

27.0

33

-6

12 cm

Same

36.4

33

3.4

12 cm

Opposite

29.6

33

-3.4

12 cm *

Same

33.0

33

0

* Indicates coils are oriented perpendicular to each other.

When the coils are connected in series with windings in the same direction, is the mutual inductance greater or lesser than twice the self inductance of a single coil? Why?

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PHYSICS 182B/196L LAB REPORT - LAB 8: FARADAY’S LAW AND INDUCTANCE

The total inductance is greater when the coils in a series have windings in the same direction. They begin to reinforce themselves and the mutual inductance increases.

When the coils are connected in series with the windings in opposite directions, is the mutual inductance greater or lesser than twice the self inductance of a single coil? Why? The total inductance is lesser when the coils in a series have windings in the opposite direction. They begin to cancel each other out and the mutuals inductance decreases.

Explain what is happening when the second coil is oriented perpendicular to the first coil (hint: explain in terms of M and the magnetic fields). The coils that are oriented perpendicular to each other have no linkage because of the connection between the different angles.

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