In this lab, we will validate Lenz' law and (qualitatively) Faraday's law, demonstrating that a change in magnetic flux generates a current opposing the change in flux.

We will also be measuring the extent to which a transformer deviates from an ideal transformer.^{Hoveroverthese!}

• 1 analog Oscilloscope
• 1 Bar Magnet
• 2 Solenoid Coils (& Steel Bar)
• 1 Galvanometer (roughly speaking, this is an analogue ammeter)
• 1 DC Power Supply
• 1 Function Generator
• 6 Leads with banana connectors
• Record data in this Google Sheets data table

Ensure you are very familiar with both uses/versions of the right hand rule: for moving charges in a magnetic field, and for EMFs induced by a time-varying magnetic field.¹

The last part of this lab deals with something you don't touch on in class: non-ideal transformers.²

For an ideal transformer, we assume that all the flux that the first loop generates passes through the second loop. Our guiding equations, by Faraday's law (neglecting signs), are:

$$V_1=N_1\frac{\delta \Phi_1}{\delta t}$$ $$V_2=N_2\frac{\delta \Phi_2}{\delta t}$$

Let's now assume that only a net fraction \(f\) of the flux passing through is going through the other coil, yielding \(\Phi_2=f\Phi_1\).¹ (assuming \(V_1\) is the generating voltage and \(V_2\) is the induced voltage). This yields the result:

$$\frac{V_2}{N_2}=f\frac{V_1}{N_1}$$

In this lab, we are therefore going to be measuring \(f\) using the equation:

$$f=\frac{V_2}{V_1}\frac{N_1}{N_2}$$

Transformers typically make \(f\) as close to one as possible using some sort of magnetizable material, which "focuses" the magnetic field inside the coil. We will measure \(f\) both with and without a steel bar inside the coil, and observe the difference.

Part I: Free Charges and a Bar Magnet

Set the Oscilloscope to XY mode (push in that button) and VERT MODE to CH2. This should cause the screen to have a single stationary dot on screen.¹ Adjust the position knobs until the dot is in the middle of the screen.

This dot results from the oscilloscope emitting a beam of electrons from the back of the machine to the front. We are going to be studying the effects of a magnet on this beam. Based on that information, fill out the first few questions.

Now, we are going to introduce the magnet. Hold up your bar magnet flat across the screen with the dotted end pointing to the left.² Observe that the beam is deflected, and record the direction in which it is deflected.

This deflection arises from a magnetic force in the direction of the deflection (i.e., if it were deflected left, the magnetic force would be to the left). Using the right-hand rule to work your way backwards to the magnetic field from the directions of velocity and magnetic force, deduce the direction of the magnetic field.²

Then, repeat the above procedure with the dotted end on the right, top, and bottom, and record the direction of deflection and direction of magnetic field for each.

Based on the above information and your knowledge of how magnets work, deduce whether the dotted or undotted end is magnetic North.³

Part II: Bar Magnet and a Coil

Now, set the oscilloscope aside (we won't be needing it again until part IV).

Take the large magnetic coil, and set it upright (such that the base sits on the table). Remove the smaller coil (and steel rod) from inside it, if necessary.

Use banana cables to wire it to the galvanometer (red to red and black to black). When you do so, use the "1500" port on the coil (which indicates that port is connected to 1500 turns away from the black "zero" port).

Insert the magnet into the coil. You should observe that the galvanometer deflects in some direction. The galvanometer measures current, so this means that the change in flux from the magnet produced a (small) current via induction.

Now, let's do it a bit more carefully and keep track of all the directions involved.

When you insert the magnet, keep track of what end of the magnet you are inserting, and the direction from which you are inserting it (presumably, from above). Based on these two pieces of information, what direction is the change in magnetic flux - up or down?

Keep in mind when thinking about that question that the magnetic field inside the magnet flows in the opposite direction as the field outside the magnet, and here, most of the change in magnetic flux comes from the field inside the magnet.

Now, insert the magnet, and observe (and record) the direction of deflection of the galvanometer (initially, before it bounces back). Note that positive (right) on the galvanometer is flowing from red to black through it, and negative is flowed from black to red through it. The solenoid will therefore be opposite this - red to black inside the galvanometer is (continuing the loop) black to red inside the solenoid, and vice versa.

Based on your galvanometer deflection and wiring, deduce what direction the current in your coil flowed. This will require knowing what direction (clockwise or counterclockwise) the coil turns when going, say, from red to black. To determine this, look closely at the wires emerging from the terminals for the banana cables.

From all of the above information, deduce the direction of the magnetic flux produced by the induced current, and whether or not this agrees with Lenz' law.

Finally, as a separate observation, try inserting the magnet more quickly. How does the magnitude of galvanometer deflection compare to the magnitude when you insert it more slowly? What if you vary the number of turns (represented by the numbers on the base of the coil)? Also, when you just leave it inside, what does the galvanometer do? What law describes these behaviors?

Part III: Electromagnet and a Coil

Now, set aside the bar magnet. Take the second coil, and wire it up to the DC power supply (red to red, and black to black, 3V or less). If you insert this coil into the other one, like the previous part, you should observe a deflection. For optimal results, you should have the steel bar inside the small coil as you insert it.

Note that the DC power supply makes a current from red to black inside the solenoid. Based on observation of the wires inside the solenoid (as in the last part), deduce whether the current flows clockwise or counterclockwise (as viewed from above, when the small solenoid is held with the same orientation you will hold it when you insert it into the large coil).

Again, insert it, and check the direction of the (initial) deflection of the galvanometer. Does the direction of deflection match what you expect based on your knowledge of Lenz' law and your results from the previous part?

Please remember to turn off the DC power supply and disconnect it from the small coil.

Part IV: Transformers

Now, unplug all previous instruments, and just look at the oscilloscope, function generator, and solenoid coils. You will now be wiring these things together (always red to red and black to black, of course).

First, insert the smaller coil within the larger solenoid coil, and the steel bar inside the coil.

Next, wire the function generator to channel 2 of the oscilloscope.

Then, in parallel with Cha 2 of the oscilloscope (so with two more wires), wire the function generator to the large coil, as well. It is best to use the 1500 turns port here.

Finally, wire the small coil to channel 1 of the oscilloscope.

Now, unpress the "XY" button, and set the oscilloscope VERT MODE to DUAL.

If you turn on the function generator (and have it set to a sine wave), you should now observe two sine waves on your screen, one for each coil.⁴

Vary the TIME/DIV and VOLTS/DIV knobs, as well as the POS knobs, until both waves show are completely on screen and show 2-5 full periods. Note that the TIME/DIV controls both waves, but the VOLTS/DIV knobs are separate for each.

Sketch the screen of the oscilloscope. Be sure to label the waves as to which is the small or large coil (tweak the POS knobs and see which one moves), and record this on your sketch.

For this sketch, you may have two different VOLTS/DIV settings, which complicates your y-axis labels. A good way to draw this is to put the CH1 voltages on the left-hand side of the plot, and the CH2 voltages on the right-hand side.

Measure the peak-to-peak amplitude of each wave (using the corresponding VOLTS/DIV settings). Record the amplitude of the wave for the larger coil as \(V_1\) and the amplitude of the wave for the smaller coil as \(V_2\) (with uncertainties). Note how many turns you are using in your larger coil as \(N_1\), and take \(N_2=175\). Take 1 turn as the uncertainty in the number of turns.

Finally, take out the steel bar, and repeat this measurement.

Make sure you answer all the questions presented as a part of the procedure above (presented on the data table).

Using \(N_1\), \(V_1\), \(V_2\), and \(N_2\), calculate \(f\), the (unknown) "efficiency" of our transformer, both with and without the steel bar.

Your TA will ask you to answer some of the following questions (they will tell you which ones to answer):

Experimental Questions:

1. Suppose we ignore the possibility of someone having miscounted the number of turns. Why might "1 turn" (or, perhaps, "1/2 turn") still make sense as an uncertainty on the number of turns?

Theoretical Questions:

1. What would happen if you increased the number of turns on the smaller coil in part III (for the same length coil)?
2. What other kinds of "losses" might exist in a non-ideal transformer?³

For Further Thought:

1. What happens to the energy in the "lost" flux?
2. Sometimes, the function generator varies in amplitude a bit when you remove the steel bar. Why might that be?

Guide to Uncertainty Propagation & Error Analysis (Quick Reference)

Notes on the Oscilloscope

Notes on the Function Generators

Spare Oscilloscope Sketch Paper