1 Faraday’s law

The purpose is to study (qualitatively) Faraday’s law and Lenz’s law of electromagnetic induction.

The apparatus is a pair of coils, a small ammeter/galvanometer, a bar magnet, a small compass, a battery or dry-cell and a battery holder, jumper wires or banana-plug wires, and a knife-switch or button switch.

1.1 Faraday and Lenz’s laws

An emf $ℰ$ will be induced in a circuit that is threaded by a time-varying magnetic ﬂux $Φ_{B}$ according to Faraday’s law

ℰ = - \frac{d}{d t} Φ_{B} = - \int_{S} B_{e x t} \cdot n d A

in which $S$ is the area enclosed by the circuit, and $\hat{n}$ is the unit normal to the circuit. This normal is established by the right-hand rule; lay the circuit on the ﬂoor, traverse the circuit in such a sense that the area enclosed stays to your left, and the normal points up.

The negative sign is Lenz’s law; the induced emf would drive an induced current $I_{i n d}$ through the circuit if it is a conductor, this current sets up a second, induced magnetic ﬁeld $B_{i n d}$ that ﬂuxes through the circuit in such a way that the total ﬂux is constant

\frac{d}{d t} \int_{S} (B_{e x t} + B_{i n d}) \cdot \hat{n} d A = 0

1.2 Calibration

You will need to determine in which direction the galvanometer deﬂects when currents pass through it. Galvanometers are sensitive, and so we never run currents through them that

would exceed the maximum deﬂection on the instrument. To guarantee this we apply a battery voltage through a large resistor, your body. Connect the battery to the galvanometer as illustrated below, but do not complete the circuit with a wire, let the two ends A and B dangle unconnected. Watch the galvanometer carefully as you pick up terminal A in one hand and B in the other, completing the circuit through your body.

The resistance through your body is millions of Ohms, so the current is miniscule. In this ﬁgure the current will enter the red galvanometer terminal and exit through the black. Your terminals may not be color coded. Record the direction of the current and the galvanometer deﬂection on the ﬁgure in the lab report, and refer to it during your analysis of the remainder of the experiment.

1.3 Induced currents

Construct the circuit illustrated below; consisting of one coil and the galvanometer. In this illustration, wires beginning at the red coil terminal wind around the coil-body clockwise as seen from this end, and exit the coils black terminal. Your coil may not be wound in this sense. Record the sense of your coils windings on the ﬁgure in the lab report.

Move the north pole of the bar-magnet towards the end of the coils as illustrated in the ﬁgure. You will need to establish which end of the magnet is magnetic north if it is not marked. This is where the compass comes into play. The bar-magnet that is the compass needle aligns itself with the magnetic ﬁeld lines that begin on the magnets north pole and end on the south.
Once the correct pole of the bar-magnet has been determined, note the response of the coil if you move the bar-magnet north pole towards or away from the coil. Record these responses in the lab report and carefully explain the behavior in terms of induced currents in the coil and Lenz’s law.
Holding the bar-magnet as shown in the ﬁgure in a ﬁxed position, rotate the coil until the hole through the center is vertical. Carefully record the response of the galvanometer. Determine the sense of the induced current and explain what you witnessed using Lenz’s law.

1.4 Induction with a primary coil

Create two circuits, one containing a coil (the primary), a battery, and a switch. Keep the switch open when the circuit is not in use. The second circuit (the secondary) contains just a coil and the galvanometer. It is important that both coils be wound in the same sense, so be careful in your construction to ensure this.
Place the two coils in close proximity to one another with the central holes aligned, as illustrated in the ﬁgure. You will study the response of the secondary circuit to changes in the current in the primary. This circuit illustrates the action of a transformer, in which the changing currents and emfs in the primary induce currents and emfs in the secondary. The relative magnitudes of the primary and secondary currents can be controlled by adjusting the number of turns of wire in the two coils.

Begin with the switch S open, and note the deﬂection of the secondary circuit galvanometer. Explain the sense of the deﬂection by carefully describing the directions of the currents in the primary and secondary coils. Explain why the deﬂection diminishes over time.
Suddenly open the witch S, and note the deﬂection of the galvanometer. Explain this behavior, and why the deﬂection relaxes to zero as time passes.
Repeat this experiment with an iron rod threaded through the two holes of the coils. Both deﬂections will be very much greater than in the absence of the rod. Explain why this is true.
Repeat this experiment with a copper or brass rod threaded through the two holes of the coils. Compare the magnitude of the deﬂection to the other two cases (no rod and iron rod). Do the same with an aluminum rod (assuming that these are all available). For which type of rod is the deﬂection the greatest? Explain why this is so.

With the switch S closed, move the primary coil away from the secondary, and note the sense of the galvanometer deﬂection. Now move the primary back towards the secondary, again noting the deﬂection. If the deﬂections are too small to be readily distinguished, try putting the iron rod through the hole in the secondary, and move the primary coil back and forth, keeping the holes aligned. Explain what you see in terms of induced currents and Lenz’s law.

1.5 Pre-lab exercises

1. On the ﬁgure below, draw arrows on the ﬁeld lines to indicate the sense (direction)

and ﬁll in the appropriate half of each compass needle to show which way these compasses will point if placed at the three locations shown.

2. Suppose that the magnetic ﬂux through a circuit is

Φ_{B} (t) = Φ_{0} sin 100 \frac{r a d}{s} t

Find the two earliest positive time values for which the ﬂux is zero. Find the two earliest positive time values for which the induced emf is zero.

3. Suppose that the magnetically-induced emf in a circuit is

ℰ (t) = ℰ_{0} sin 100 \frac{r a d}{s} t

Find the two earliest positive time values for which the ﬂux is zero. Find the two earliest positive time values for which the induced emf is zero.

1.6 Lab report

Faraday and Lenz’s law


Experimenter 1		Experimenter 2

Experimenter 3		Experimenter 4

Calibration. Carefully draw currents entering and leaving the terminals of the galvanometer, and draw the needle indicating the direction of its deﬂection with this current.

Induced currents. Set up the coil and galvanometer so that it is wound in the same sense as seen from the front as in the ﬁgure. Draw the induced current direction in the wire and the galvanometer deﬂection as you move the bar-magnet north pole towards the coil. Explain your observations.

Induction with primary coil. Draw the needle deﬂection and induced current in the secondary coil (left) when the switch S on the primary is closed. Explain your observations.

Induction with primary coil. Draw the needle deﬂection and induced current in the secondary coil (left) when the switch S on the primary is opened. Explain your observations.

Draw the induced current in the secondary and the galvanometer deﬂection when the primary is moved away from the secondary, with the holes aligned. The primary is behind the secondary in this ﬁgure.

Draw the induced current in the secondary and the galvanometer deﬂection when the primary is moved towards from the secondary, with the holes aligned. The primary is behind the secondary in this ﬁgure.

Draw the induced current in the coil and the galvanometer deﬂection when the north pole of the magnet is held at a ﬁxed position, and the coil is rotated by

9 0^{o}

(until central hole is vertical).

Record and explain the your observations on the relative sizes of the galvanometer deﬂections when the various different rods are inserted through the aligned holes in the coils.