PHYS 1402 – General Physics II

Faraday's Law

 

Leader: _________________________          Recorder: __________________________

Skeptic: _________________________         Encourager: ________________________

 

Materials

Galvanometer                                                   Compass

200, 400, and 800 turn coil                               Genecon

Cow Magnet                                                    Analog DC voltmeter

2 x banana plug cable                                       Bar Magnet

6 x alligator clip wire                                         Stop Watch

 

Introduction

      When Michael Faraday first heard of Hans Christian Oersted's discovery of electromagnetism in 1820, he was intrigued.  In electromagnetism, a current produces a magnetic field.  Faraday wondered could the opposite happen?  Could a magnetic field cause a current?  He spent 11 years searching until when disassembling an apparatus after an unsuccessful experiment, he found what he was seeking.

 

Part 1 Faraday’s and Lenz’s Law

Procedure and Questions

1.  Set-up

Note:  For a later section of this activity it is important that you connect the apparatus as specified.  This activity will make use of a galvanometer.  A galvanometer is a very sensitive ammeter.  You’ll note that the terminals on the galvanometer are labeled + and

 -.  When current flows into the + terminal and out of the – terminal, the needle will deflect to the right, and when current flows in the opposite sense the needle will deflect to the left.  Notice how the turns are oriented on the 200 turn coil.  Position the coil so that it is in front of the galvanometer with its opening perpendicular to the face of the galvanometer, and orient the coil so that the turns go round in a right hand sense.  Connect the front of the coil to the + terminal on the galvanometer and the back of the coil to the – terminal on the galvanometer.

      Use the compass to identify the N and S pole of the cow magnet.  Remember the N pole of a magnet will repel the N pole of the compass.  But you can’t bring the strong cow magnet too close to the compass or it will overwhelm it.  Label the N pole of the magnet fro reference.

 

2.  Observations

Quickly insert the N pole of the cow magnet into the coil and observe the needle of the galvanometer.  Quickly pull the magnet back out and observe the needle of the galvanometer.

 

Q1)  What  happened to the needle of the galvanometer when the magnet was inserted?

 

 

Q2)  What happened to the needle of the galvanometer when the magnet was pulled back out?

 

 

Reverse the direction of the magnet and try again.

 

Q3)  Did you see any difference when you reversed the orientation of the magnet.

 

Repeat your observations for both orientations on the other side of the coil and summarize your results in the table below.  You should have a total of 8 observations.  Leave the last two columns blank for now.

 

Side of Solenoid

(Front or Back)

Pole

(N or S)

Direction of Magnet

(into or out of the solenoid)

Direction of Needle on Galvanometer

(R or L)

Sign of current

(+/-)

Induced

Pole

(N/S)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q4)  List the cases where the galvanometer needle deflected to the left and to the right in the space below.

 

 

 

 

 

 

 

Q5)  Sketch diagrams for the cases where the galvanometer needle deflected to the left.  Be sure to indicate the orientation of the magnetic field and the direction of travel of the magnet.  Use your diagrams to explain how the situations that produced a deflection to the left are similar.

 

 

 

 

 

Q6)  Sketch diagrams for the cases where the galvanometer needle deflected to the right.  Be sure to indicate the orientation of the magnetic field and the direction of travel of the magnet.  Use your diagrams to explain how the situations that produced a deflection to the right are similar.

 

 

 

 

Q7)  If the magnet just sits inside the coil, do you see any deflection of the galvanometer?

 

 

Q8)  What is happening to the magnetic field in the coil when you do see a deflection of the galvanometer needle?

 

 

Question 8 is the essence of Faraday's law and why it was so difficult for Faraday to find it.  In his experiments Faraday had used steady magnetic fields to try and produce a current, but it is a changing magnetic field that produces a current.

 

Lenz's Law

      You should have noticed that there is a pattern when the deflection of the needle of the galvanometer is to the left or the right.  The result is known as Lenz's law.

 

Identify the terminals labeled + and – on the galvanometer.  When a positive current flows into the terminal labeled +, it will produce a deflection of the galvanometer needle to the right. 

      Identify for each of your observations whether the current is + or – nd fill in the last column of the table above.

 

Q9)  When you insert the magnet in the coil you produce a current.  What does a current in a coil produce?

 

 

 

Q10)  Use the direction of current flow in the coil and your right hand rule for a solenoid to determine the direction of the magnetic field induced by the current for each of the eight observations you made above.  Use the direction and label the pole induced on the side of the coil where the magnet is being moved.

 

 

 

Q11)  In all cases when you inserted a N pole, what pole was induced on the side where you inserted a N pole?

 

 

Q12)  Would the induced pole try to attract or repel the inserted N pole?

 

 

Q13)  In all cases when you removed a N pole, what pole was induced on the side where you removed a N pole?

 

 

Q14)  Would the induced pole try to attract or repel the removed N pole?

 

 

Q15)  In all cases when you inserted a S pole, what pole was induced on the side where you inserted a S pole?

 

 

Q16)  Would the induced pole try to attract or repel the inserted S pole?

 

 

Q17)  In all cases when you removed a S pole, what pole was induced on the side where you removed a S pole?

 

 

Q18)  Would the induced pole try to attract or repel the removed S pole?

 

 

Q19)  Note that whenever you inserted a pole a like/opposite (circle one) pole was induced, which would attract/repel (circle one) the inserted pole.

 

Q19)  Note that whenever you removed a pole a like/opposite (circle one) pole was induced, which would attract/repel (circle one) the removed pole.

 

Q20)  Lenz's law is the observation of how the direction of the induced field compares to the direction of the inducing field.  The directions are _____________.

 

 

Magnetic Flux

      So far we have only investigated a single magnet and coil.  Let us investigate other factors that might affect the induced current.

 

Q21)  Try a weaker magnet.  How does the effect compare.

 

 

Q22)  Connect a coil with 400 turns.  Try again with the cow magnet.  How does the effect compare?

 

 

Q23)  Connect a coil with 800 turns.  Try again with the cow magnet.  How does the effect compare?

 

Use the alligator clip wire to make a coil with 10 turns and connect it to the galvanometer.  Insert the magnet and note the size of the effect.

 

Wrap a coil again with 10 turns only make the radius of the coil half as big.

Insert the magnet and note the size of the effect.

 

Q24)  How did the effect compare when the coil had half the radius?

 

 

You should have observed that the induced current was smaller if the magnet was weaker, the number of turns was less and the area was smaller.  This combination of variables produces what is called the magnetic flux.  The magnetic flux through a single coil is defined as FB  = B×nA, where n is a unit vector perpendicular to the area.   Remember that a dot product is defined as  B×nA = BA cosq.  If the magnetic field goes through N coils, then the total flux is simply Ftot = NFB .  When you insert the magnet into the coil, you change the flux because you change the magnetic field.

 

Q25)  Are there any other ways to change the flux?

 

 

Q27)  Try connecting a single piece of flexible wire across the terminals of the galvanometer.  Wrap three or four turns loosely around one end of the magnet.  Rapidly pull the ends of the wire so that you collapse the coil.  Do you observe an effect? (Note you will need to observe very carefully.)

 

 

Q28)  In Q27 we saw that we could induce a current by changing the area.  However what are we actually producing when we change the flux?  Find the SI units of

DFB /Dt.  What kind of quantity has these units?  Hint:  what do you need to produce a current?

 

 

 

 

You should have found in Q28) that the units of the rate of change of magnetic flux are V, so  we can sum up Faraday's law as the following:  DFB /Dt = -E, where we have denoted – as is customary – the induced potential by E for EMF.  The – sign in Faraday's law is Lenz's law.  It means that the induced voltage is such as to try and oppose the change in magnetic flex.

 

Q29)  Faraday's law can be summed up as A _______________ magnetic flux induces a/an ________________________, which __________________ the change.

 

Part 2  The Electrical Generator

Introduction

      In Part 2 we will partially examine the proportionality between the induced EMF and the rate of change in the magnetic flux.  We will make use of the Genecon.  The Genecon turns, via a gear system, a coil in a magnetic field.  Figure 1 shows a schematic of the geometry.  The cross sectional area of the coil, through which the field lines cross, is a function of the angle between the coil and the field lines.  When the angle is 90 degrees the cross sectional area is zero and it is the entire area of the coil when the angle is 0 degrees.  Thus we can write the magnetic flux as .

If we turn the coil at a constant angular rate, , then the angle is given by *,

and thus the flux is given by .  It can be shown, using calculus, that the rate of change of the magnetic flux and thus the average induced EMF is given by

                    Equation 1

      In the Genecon the only variable on the right hand side of Equation 1 that we have access to is the rate at which the coil is turned.  Thus, we will investigate the proportionality between the induced EMF and the rate of change of the magnetic flux by examining the proportionality between the induced EMF and the rate at which the crank is turned.

 

Procedure

Begin by connecting the Genecon between the (+) terminal and the (-) terminal marked 15 V on the analog voltmeter.  Turn the crank such that the meter reads a positive voltage.  (Note:  If this is an uncomfortable direction to turn the crank, simply reverse the connections between the Genecon and the voltmeter.)  Our procedure will be to turn the crank such that we get a specified voltage and to determine the rate at which we are turning the crank.  We will determine the rate at which we turn the crank by simply timing ten turns.  The frequency at which we turn the crank is then given by

 where t is the time required for 10 turns of the crank.

The rate at which we turn the crank is then given by  .

      Turn the crank at a steady rate such that you get a voltage of 1 V on the meter.

1.      Record the time it takes to complete ten turns of the crank.


2.      Calculate the frequency, , and the angular frequency .


Increase the rate at which you turn the crank so that voltage reads 2 V and determine the rate at which you are turning the crank.  Repeat your measurements three more times each time incrementing the voltage by 1 V.  Record your measurements, including the first in the table below.

3.       

Table 1            Data for the Voltage as a function of the Frequency

Voltage, V (V)

Time for 10 turns, t (s)

Frequency,  (Hz)

Angular Frequency

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1          Geometry of generator

 

Data Analysis

4.      For Part 2 of the lab, the data analysis is very straightforward.  Using either Excel or Graphical Analysis for Windows, plot the induced EMF versus the angular frequency at which you turned the crank.  Draw the best-fit line that goes through your data points and determine the slope of the line, including units.  We need to make a slight adjustment to the result given by Equation 1.  The rate at which we turn the crank is not the same as the rate at which the coil is turned because of the gearing within the Genecon.  Thus we need to add the gear ratio to our result.  We thus expect our model to be  where  is the gear ratio.  Our graph of  vs.  should be a straight line with a slope .  Attach your graph to your worksheet.  (Note:  The gear ratio of the genecon is 48:1.)

5.      Does this slope have a reasonable value?  Explain your reasoning.



6.      Explain in what way this graph demonstrates Faraday’s Law?