Generating induced currents Teach article

Author(s): Antxon Anta, Elizabeth Goiri

Three simple experiments illustrating Faraday’s law of induction and the different ways induced currents may be generated.

In this article, we present a series of simple classroom experiments that allow students to observe magnetic induction phenomena directly and apply their knowledge of induced currents to explain them.

*Image adapted from Watthana Tirahimonch*/*AdobeStock, Standard License*

When students are able to interact directly with the subject matter, they are more engaged, involved and motivated. This leads to a more gratifying and effective learning and teaching experience for students and teachers. As the old Chinese proverb goes, “I hear and I forget; I see and I remember; I do and I understand”.

The activities are aimed at students aged 16 to 19. We recommend that students carry out the experiments in groups of three and then discuss their results before presenting them to the whole class.

After completing this activity, students should

understand Faraday’s law of induction from an experimental point of view;
understand Lenz’s law from an experimental point of view;
understand the relationship between variations in magnetic flux and the induced electromotive force (EMF);
know how induced currents can be generated.

Historical background

Back in 1831, the English scientist Michael Faraday discovered that it was possible to generate electricity by means of motion in a magnetic field. He also demonstrated how a current in one circuit could induce a current in a neighbouring circuit. He soon explained this phenomenon in terms of variation in magnetic flux. The following year, in 1832, the American scientist Joseph Henry made similar observations independently.

These findings eventually led to the formulation of Faraday’s law of induction, which is now one of the four fundamental laws of electromagnetism. This law states that the electromotive force Ɛ induced in a circuit is proportional to the rate of change of the magnetic flux through the circuit. Faraday’s law is expressed mathematically as follows:

The minus sign on the right-hand side of the equation indicates that the direction of the induced current generates a field that opposes the change in the magnetic flux that caused the current in the first place (Lenz’s law).

There are different ways to change the magnetic flux through a circuit and, consequently, various ways in which a current can be induced. We will explore these in the proposed activities.

Magnetic flux

The magnetic flux (Ø ) through a given surface can be thought of as the number of magnetic field lines that pass through it.

Figure 1: a) The magnetic field $\vec{B}$ penetrates a closed flat loop with the surface vector $\vec{S}$ . b) The magnetic field $\vec{B}$ penetrates a differential surface element d $\vec{S}$ on a curved surface.
*Images: a) Image courtesy of the authors; b) Image adapted from Maschen/Wikimedia Commons*, *CC0 1.0*

Consider a flat loop described by a surface vector $\vec{S}$ , where the magnitude of this vector is equal to the loop’s surface area and the vector’s direction is perpendicular to the loop. In the presence of a uniform magnetic field $\vec{B}$ , the flux through the loop is expressed as the scalar product of $\vec{B}$ and $\vec{S}$ :

Where θ represents the angle between $\vec{B}$ and $\vec{S}$ (see figure 1a).

If we have a coil of N turns instead of a closed loop, the magnetic flux will increase N-fold, as the magnetic field penetrates each of the loops forming the coil:

When the magnetic field is non-uniform and the surface through which the flux must be calculated is not flat, the surface can be divided into small parts represented by d $\vec{S}$ . This so-called differential surface element, d $\vec{S}$ , is small enough that we can consider that the magnetic field through it to be constant (see figure 1b). The flux differential dØ through d $\vec{S}$ is therefore:

The flux through the entire surface is equal to the sum of all the flux differentials dØ through their respective differential surface elements and can be obtained by integrating:

Combining this equation with Faraday’s law, we can see that a current can be induced in a closed loop in any of the following ways:

by varying the magnitude of the magnetic field B;
by varying the size of the coil (i.e., S );
by varying the relative orientation of $\vec{B}$ and $\vec{S}$ .

Activity 1: Varying the magnetic field

In this activity we will induce an electrical current by changing the magnitude of the external magnetic field.^[1,2]

Materials

Three PVC tubes (length: 53 cm; outer diameter: 3.9 cm; inner diameter: 3.2 cm)
Three stacks of three cylindrical neodymium magnets (magnet size: 28.5 mm × 10 mm)
Coils made from enamelled copper wire (wire diameter: 0.5 mm; coil diameter ca. 4 cm). See supplementary materials for tips on how to assemble the coils.
- 3 x coil of 110 turns 1 x coil of 230 turns
- 1 x coil of 400 turns
Three 3 V flashlight bulbs
Three lightbulb sockets
One red LEDs
One green LED

Procedure

Experiment A

Take the three coils that have the same number of turns.
Connect the ends of each coil to the light bulb sockets, then screw in the 3 V bulbs.
Attach the coils to the ends and the middle of the PVC tube, as shown in figure 2a.
Hold the tube upright and drop a magnet through the tube.

Observation: As the magnet falls through the tube with the three coils, the light bulbs are observed to flash one after the other. The intensity of each successive flash increases.

Explanation: Due to the uniform accelerated motion of the falling magnet, its velocity – and therefore the change in flux through each successive coil – increases as it falls.^[3]

Figure 3: The diagram shows that the intensity of flash increases with the velocity of the falling magnet in experiment A.
*Image courtesy of the authors*

Experiment B

Take three PVC tubes of the same length and attach a different coil (400, 230 or 110 turns) to the bottom of each tube, as shown in figure 2b.
Connect the ends of each coil to the light bulb sockets and then screw in the 3 V bulbs.
Holding the tubes upright, drop a stack of magnets through each tube simultaneously.

Observation: The falling magnets produce flashes of different intensity in each of the three tubes. The greater the number of turns, the more intense the flash.

Explanation: The magnetic flux, and therefore the induced current and the intensity of the flash, is proportional to the number of turns in the coil.

Figure 4: The diagram shows that the intensity of flash increases with the number of turns of the coils in experiment B.
*Image courtesy of the authors*

Experiment C

Attach the coil with 230 turns to the bottom end of the PVC tube.
Connect the coil to a red and a green LED in parallel, but in opposite orientations.
Drop the stack of magnets through the tube.
Drop the stack of magnets through the tube again, this time orienting the magnet stack in the opposite direction. Mark one side of the stack with a marker or sticker to keep track of the orientation.

Observation: When the magnet is dropped through the tube, the red and green LEDs flash quickly in succession, not simultaneously. When the orientation of the magnet is reversed, the order of the flashes changes (red-green vs green-red).

Explanation: The change in flux is positive (i.e., flux increases) when the magnet approaches the coil, and negative (i.e., flux decreases) when it moves away from it. Therefore, the induced current first flows in one direction, allowing only one of the LEDs to flash, and then in the other direction, causing the other LED to flash (see figure 5). (The two LEDs are connected in opposite orientations).

Figure 5: The diagram demonstrates what happens in experiment C. The LED flashes green (red) at time t as the magnet approaches the coil and red (green) as it falls away from it an instant later at t’.
*Image courtesy of the authors*

Discussion

The following questions can help you evaluate how well the students have grasped the concepts:

Regarding experiments A and B:
- Why do the light bulbs flash?
- Do all the light bulbs flash with the same brightness?
- Which light bulb flashes the brightest? Why?
- What is the magnitude of the induced EMF?
Regarding experiment C:
- Do the red and green LEDs flash simultaneously?
- Which LED flashes first? Why?
- Does the orientation of the stack of magnets make a difference? Why?
- What is the magnitude of the induced EMF?

A detailed discussion of the experiments can be found in the explanation sheet 1 in the supplementary materials.