Faraday’s Law – Electromagnetic Induction

Figure 1: Electroscope setup

Figure 2: Oscilloscope setup

Two versions of how to demonstrate electromagnetic induction are available.

  1. The “classic” version, shown in Figure 1, can be performed by quickly inserting and removing a magnet into the coil. The electrometer shows the value and direction of the induced current.
  2. The “modern” version, shown in Figure 2, requires an oscilloscope with memory capabilities. It displays the induced voltage of the inductor and displays it on the oscilloscope screen for several seconds for students to view. It is possible to display either a pulse or oscillation as shown below in Figure 3 and Figure 4 respectively. A magnet is dropped through the solenoid to create the pulse, or moved in and out repeatedly to create an oscillation.

A video camera should be used to display both oscilloscope screens or electrometer values so that students can see on the big screen.

Figure 3: Ideal oscilloscope capture for a pulse

Figure 4: Ideal oscilloscope capture of an oscillation

Equipment:

  • Solenoid/Inductor [Cabinet F4]
  • Electrometer or Oscilloscope [Cabinet F2 and K1 respectively]
  • Bar Magnet and Neodymium magnets [Cabinet F3]
  • Banana Cables
  • Banana to BNC connector [Left of cabinet K]
  • Sandbag [Cabinet A3]
  • Jacks or stand

Demo:

Classical Version

    • Attach the solenoid to a stand, such that the bar magnet can easily pass through the center of the solenoid.
    • Attach the electrometer in parallel to the solenoid.
    • Move the bar magnet through the solenoid.

As the bar magnet approaches and recedes from the solenoid, you should see the electrometer detect a quick change in electrical potential difference. This is caused by the induced voltage, or electromotive force (emf), from the bar magnet’s magnetic field interaction with the solenoid by Faraday’s law. A slower moving bar magnet close near the solenoid creates a weaker emf, while a faster moving bar magnet creates a stronger emf.

Modern Version

  • Attach the solenoid to a stand, such that the bar magnet can easily pass through the center of the solenoid.
  • Connect the solenoid to channel 1 on the oscilloscope using the banana cables or BNC to banana cable shown in Figure 2.
  • Change the scale settings to a timescale of 500 ms and a voltscale of 2V.
  • To pause the screen, push the run/stop button in order to view a single pulse in greater detail.

When the bar magnet approaches and recedes from the solenoid, you should see a sinusoidal wave on the oscilloscope. If you move the magnet quick enough, you should be able to create a single sinusoidal pulse wave. A faster moving magnetic near the solenoid will create a sinusoidal wave with a greater amplitude and shorter wavelength. A slower moving magnet will result in a lower amplitude and longer wavelength for the generated sinusoidal wave.

Explanation:
Michael Faraday discovered that an electromotive force \varepsilon, or emf, is induced in a circuit and is caused by a change of magnetic flux (\Phi_B) through the circuit:

\varepsilon = - \frac{d \Phi_B}{dt}

where the magnetic flux is given by:

\Phi_B = \vec{B} \cdot \vec{A} = BAcos(\theta)

This states that the magnetic flux, or the amount of magnetic field passing through a surface area, depends on the strength of the magnetic field \vec{B}, the perpendicular cross-sectional area \vec{A} of the coil of wire, and the angle \theta between them. The magnetic flux is also given by:

\Phi_B = \int \vec{B} \cdot d\vec{a}

where we are summing over all of the infinitesimal areas \int d\vec{a} in which the magnetic field \vec{B} is aligned with. This alignment is given by the dot product of the magnetic field and the infinitesimal area is being investigated.
When the magnetic flux undergoes a change, it results in an induced voltage, or emf, on the coil of wire.

In this demonstration, a bar magnet is used as the source of the magnetic field. As the bar magnet approaches the solenoid, or the coil of wire, the magnetic field flowing through the coil of wire increases. This causes a change in magnetic flux , which induces an emf in the coil of wire. However, there will not be an induced current since the setup for this demo does not contain a closed loop of wire; the ends of the solenoid are directly connected to  either an electrometer or an oscilloscope.

The direction of the induced voltage, and potentially the flow of the induced current if this were a connected loop, is determined by Lenz’s law. Lenz’s law asserts that a current created by an induced emf in a wire travels in a direction such that the magnetic field created by the induced current opposes the original change in flux.

In the example where the north pole of the bar magnet approaches the coil of wire, the induced current will travel  clockwise, and hence the induced magnetic field directed downwards. Now when the north pole bar magnet is moved away from the coil of wire, the induced current will travel in the counter-clockwise direction, which produces a magnetic field that points upwards.

The induced voltage can be measured by an electrometer or oscilloscope. The induced current can be measured by an ammeter or oscilloscope. If you move the bar magnetic’s axis parallel to the axis of the solenoid, you will get the maximum magnetic flux. This will result in the maximum emf or the maximum current flowing through the wire. If you move the bar magnet at any other angle through the coil of wire, you will notice a lower amount of current flowing through the wire. If you move the bar magnet towards the solenoid such that its axis is perpendicular to the axis of the solenoid, it would result in zero emf.

Written by Ryan Dudschus
Edited by Noah Peake