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Investigation 6...

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PHYS1110

Investigation 6

Investigation 6: Magnetic fields, the Earth, Faraday’s law and generators Aim This experiment aims to investigate the magnetic field of a bar magnet and the Earth by proceeding several simulations, and demonstrate Faraday’s law of induction and study how a generator works

Risk assessment This experiment is a simulation. There are no risks associated with it.

Part 1: Magnetic field of a bar magnet and the Earth

Results and analysis Distance (cm) 1 2 3 4 5

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Magnetic field strength (G) 13.70 3.88 1.72 0.92 0.57

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Investigation 6

Figure 1:

Magnetic field strength vs Distance 16

Magnetic field strength (G)

14

f(x) = 14.37 x^-1.97

12 10 8 6 4 2 0 0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Distance (cm)

Figure 2:

Magnetic field strength vs 1/Distance^2 16

Magnetic field strength (G)

14 12 10 8 6 4 2 0

0

0.2

0.4

0.6

0.8

1

1.2

1/Distance^2 (cm)

Relationship between magnetic field strength and distance From Figure 1, the relationship between the magnetic field strength and distance can be fitted by a inverse function line. To achieving the graph with linear fit, change x-axis to 1/distance^2 as shown in figure 2. It can be seen that the magnetic field strength and distance has an inverse square relationship.

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Relationship between the field lines inside and outside the magnet

The above diagram shows how magnetic fields flows inside and outside the magnet. The field lines outside the magnet flow from north pole and eventually converge on south pole. For field lines inside the magnet, they flow from south pole and point straight towards north pole.

Magnetic field lines around the Earth

From diagram above, it can be seen that the magnetic field lines around the Earth is similar to magnetic field around bar magnet. The field lines flow from north pole to south pole.

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Inclination and declination Magnetic inclination is the angle made by a compass needle when the compass is held in a vertical orientation. Magnetic declination is the angle made between the true north of earth magnetic field direction and the direction of the needle of the compass that is pointing at. The diagram above shows the direction of the magnetic field lines at Sydney, which is the magnetic inclination in Sydney, approximately to be -70°. From research on internet, the magnetic inclination and declination in Sydney is -64°20’36“ and 12°31’29“ respectively[ CITATION Ngd18 \l 3081 ].

Part 2: An electromagnet Results and analysis

Voltage (V) 2 4 6 4 Yifan Xiao

Magnetic field strength (G) 25.31 50.62 75.94

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101.25 126.56

Magnetic field strength vs Voltage 140

Magnetic field strength (G)

120 100 80 60 40 20 0

1

2

3

4

5

6

7

8

9

10

11

Voltage (V)

Prediction: Substitute the formula I = B=

V R

into

B=

μ0 I 2 πr

, we can get:

μ0 V 2 πrR

μ0 can be assumed as a constant. Therefore, as voltage(V) increase, 2 πrR the magnetic field strength(B) increase in a constant rate. Result: From the graph above, The magnetic field strength and voltage has linear relationship, the gradient is constant at approximately 12.66. This result does meet my expectation. In this simulation,

replace the battery with an AC source Prediction: The direction of the magnetic field will be repeatedly reverse after a certain period where the period is associated with AC generator's frequency. Observation: The observation is the same as prediction. Except for the magnetic field strength is increasing or decreasing gradually nor discretely. But this difference depends on the wave that is generated by AC generator.

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Part 3: Electromagnetic induction Description When the magnet dragged through the coil, the bulb light for a second and then become dark again. As the North pole of bar magnet starting to move towards the coil, the magnetic flux cutting the coils which induce a current into the coil. The direction of the current produces a north pole on the left-hand side (the side that is closer to magnet) to oppose the movement of the magnet towards the coil. As the North pole of bar magnet starting to move away from the coil, the magnet induces a current into the coil in opposite direction compares to the magnet coming into the coil. The current produces a north pole on the right-hand side to oppose the movement of the magnet away from the coil.

Part 4: A transformer Similarities and differences The coil with the battery attached act similar as the bar magnet, the light bulb illuminated when coil with battery or bar magnet dragged through large coil. Similarities: When they are approaching and leaving the transformer, they are inducing a current into the coil of transformer that will oppose the change of the magnet's movement. Therefore, the transformer's induced current will produce a pole that resist the magnet's movement. Differences: The bar magnet has a constant magnetic field strength. However, the magnetic field strength for the coil with battery can be changed by the voltage of DC power and number of turns of small coil. It can be said that transformer is acting more flexible than bar magnet.

Prediction when attach the AC power Since the alternating current source produces alternating current which produces a constantly changing polarity according to right hand grip rule. It means the bar magnet is switching between south and north pole constantly. The switching between poles means the magnetic flux will be changing all the time. When placed near the transformer, the constantly changing magnetic flux cutting the coil of transformer all the time and therefore, it will induce a current that is alternating in the coil of transformer, and hence the voltage will be alternating between positive and negative voltage as well.

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Part 5: Generator AC or DC voltage The generator generating AC voltage. The water causes the wheel to turn which in term rotating the magnetic field constantly. This means the magnetic flux is changing all the time. When the transformer is placed near the wheel, it will experienced a constantly changing magnetic flux cutting its coil. It will induce a current that is moving back and forth to oppose the change of magnetic field, hence the voltage is oscilating between positive and negative reigen. Which is an evidence of Alternating Current.

Lists of factors affecting the voltage for parts 3, 4 and 5 Factors affecting size of generated voltage Other factors (if Factor 1

Factor 2

Factor 3

you can think of any)

Part 3: Electromagnetic induction

The magnetic field strength

Number of turns of the coil

The velocity of magnet being dragged

The area of coil

Part 5: Generator

of small coil Number of with battery turns in

large coil

being dragged

small coil

The water flow rate

The area of coil

The magnetic field strength

Number of turns in large coil.

Use Faraday’s law to explain why each factor affects the voltage:    

generated voltage

direction of magnet being dragged The

Number of The voltage turns in of the AC power

affecting sign (+/-) of

The

The velocity Part 4: Transformer

Factors

direction of small coil with battery being dragged Change in polarity of magnet

ξ=V =−N

d ΦB dt

ξ is the electromotive force N present the number of turns in coil dt is change in the time d ΦB is change in magnetic flux, Φ B=BA cos θ (where B is the magnetic field strength, and A is the area of coil)

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From the equation, it can be seen that the change in voltage will affected by number of turns in coil, change in manetic flux and change in time. Part 3: The change in magnetic field strength will cause the change in magnetic flux and influence d ΦB , which cause generated voltage to change. The number of turns in coil directly affect size of generated voltage. The velocity of magnet being dragged affect the time for magnetic flux to change, which affect dt in the equation and lead to change in generated voltage. The change in area of coil will cause the change magnetic flux which affect d ΦB and cause change in size of generated voltage. The magnetic flux is a vector, the change in direction of bar magnet being dragged will cause change in direction of magnetic flux, which result in change in sign of generated voltage. Part 4: The number of turns in large coil directly affect size of generated voltage. The change in voltage of the AC power leads to change in magnetic field strength, which affect magnetic flux and d ΦB , and result in change in voltage. The change in velocity of small coil with battery being dragged affect the time for magnetic flux to change, which affect dt and size of generated voltage. The change in number of turns in small coil leads to change in magnetic field strength, which affect magnetic flux and d ΦB , and result in change in voltage. The magnetic flux is a vector, the change in direction of small coil with battery being dragged will cause change in direction of magnetic flux, which result in change in sign of generated voltage. Part 5: The change in magnetic field strength will cause the change in magnetic flux and influence d ΦB , which cause generated voltage to change. The number of turns in coil directly affect size of generated voltage. The change in water flow rate lead to change in spinning speed of bar magnet, which affect the time for magnetic flux to change, and result in change in voltage. The change in area of large coil will cause the change magnetic flux which affect d ΦB and result in change in voltage. The magnetic flux is a vector, the change in polarity of magnet leads to change in direction of magnetic field strength, it will cause change in direction of magnetic flux, which result in change in sign of generated voltage.

Conclusion In conclusion, this simulation investigate the magnetic field lines inside and outside the bar magnet and the magnetic field around the Earth. The magnetic field lines around the Earth is 8 Yifan Xiao

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similar to magnetic field outside the bar magnet which flow out from north pole and eventually converge on south pole. Moreover, this investigation demonstrates factors affecting size of generated voltage for electromagnetic induction, transformer and generator by using Faraday’s law ( ξ=V =−N

d ΦB ). dt

Bibliography Ngdc.noaa.gov, 2018. NCEI Geomagnetic Calculators. [Online] Available at: https://www.ngdc.noaa.gov/geomag-web/#igrfwmm [Accessed 2 Feb 2018].

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