Examples of Faraday's Law with a fixed loop in a changing magnetic field, and for a loop with changing area in a constant magnetic field.

Discussion of a 1996 experiment in which NASA attached a 20 kilometer conducting wire to the space shuttle and measured the induced current as it flew through space.

Definition, including primary and secondary coils and equations for the voltage and current relative to the number of windings in each coil. How transformers are used to step the voltage up and down in power lines that transfer electricity.

Showing the voltages in a transformer with a 220 winding primary coil and a 1 to 4 winding secondary coil. Showing that huge currents can be produced using transformers by melting a nail with a single winding secondary coil.

How transformers are used to create huge voltages and sparks from a 12V car battery. Includes a demonstration.

Step-up and step-down transformers, with equations relating that ratio of voltage and current to the ratio of the number of turns in the two coils.

Definition, including the properties of diamagnetic materials.

The properties of paramagnetic materials, including a comparison to diamagnetism.

Definition, including discussion of domains in ferromagnetic materials. Comparison between paramagnetic and ferromagnetic materials.

Showing the strength of the attraction between ferromagnetic materials and magnetic fields using a 15kg metal bar which is sucked into the magnetic field of a solenoid. Illustrating the concept of ferromagnetic domains using an array of compass needles.

Hearing the domains in a ferromagnetic material flip by connecting an amplifier to a solenoid wrapped around the ferromagnetic material and then approaching it with a magnet.

Definition, including characterization for diamagnetic, paramagnetic, and ferromagnetic materials. The Curie point for ferromagnetic materials is also defined.

Showing that an iron washer is no longer attracted to a magnet when heated above the Curie point for iron.

Showing that liquid oxygen, although paramagnetic, will be attracted to a strong magnet.

The properties of each, including the Curie temperature and the magnetic field in a solenoid with ferromagnetic material inside.

Introduction to the concept that a changing magnetic field can induce a current.

Showing that a current is induced in a coil of wire when a bar magnet is moved near or away from it.

Derivation of Faraday's Law, with a statement of the four almost complete Maxwell's Equations.

Conventions for choosing the direction of dA, explanation of why any open surface can be used, and listing of steps for using Faraday's Law.

Showing that a current will be induced in a loop of wire wrapped around a solenoid when a current is run through that solenoid. Also shows that the induced current increases when there are more loops wrapped around the solenoid.

If there is changing magnetic flux through a circuit, Kirchhoff's rules no longer apply because the electric field through the circuit is no longer conservative. In this nonconservative field, the potential difference depends upon the path.

Showing that different voltages can be measured across the same points in a circuit when there is an induced current through the circuit.

Quick review of Faraday's Law for a conducting loop in a magnetic field. Can change the flux through the loop by changing the area of the loop, the strength of the magnetic field, or the angle between the loop and the field.

Worked example of Faraday's Law with a changing angle between the loop and the magnetic field.

Showing that a current is induced in a coil of wire when it is rotated in the magnetic field of the earth.

Brief discussion of how electric generators work, as well as differences in voltage and frequency of electricity delivered in the US and in Europe.

Student tries to light up light bulbs with a hand powered generator. Also an example of a flashlight and a radio which each have a built in generator.

Worked example of Faraday's Law with a conducting loop that has changing area.

Definition of magnetic braking, with a demonstration of a copper pendulum swinging through a magnetic field.

Showing that a bulb connected to a coil of copper wire lights up when the coil is moved into or out of a magnetic field.

Showing that a conducting ring slows down as it is falling into or out of a magnetic field.

Definitions, with examples of tools that use induction motors including the table saw and lawnmower.

Showing the behavior of bar magnets, a conducting egg, and a conducting ring when placed in the magnetic field of a three phase generator.

Discussion of the secret top and how it works, with a repeat of the demo from a previous lecture.

Definition, with a demonstration of a coffee can rotating in the magnetic field of a two phase generator.

Definition, with explanation of the original discovery of superconductors.

Using a superconductor to levitate a magnet, including a demo.

How magnets are being used to create very fast, almost frictionless trains.

Running alternating current through a coil of wire above a conductor. Includes demonstration and levitation of a "woman."

Visualizations of a falling magnet and a jumping ring, which demonstrate the property of electromagnetic induction. Additional diagrams and visualizations of induction, leading to Lenz's Law that currents induced by changing magnetic flux will create magnetic fields that oppose the change in flux that induced them.

Statement that a changing magnetic flux induces an EMF. EMF is defined with diagrams. Examples of the ways to induce an EMF: Change B, change A enclosed by the loop, change angle between B and the loop. Link to visualization demonstrating these three cases. Statement of the four Maxwell's equations (almost complete).

Review of Faraday's and Lenz's Laws with a visualization and an example of a conducting ring moving over a dipole.

Explanation of eddy current braking, with link to a video demonstration.

Finding induced current and power in a simple electric generator.

Finding the magnetic field, electric field, and Poynting vector between two long sheets of current.

Statement of Faraday's Law and Lenz's Law, with diagrams and equations. Magnetic flux is defined, and ways to change magnetic flux are described with a diagram.

Review of Faraday's Law, with a list of real world applications. Mutual inductance is defined, with equations and the example of a transformer.

Explains how Faraday's Law leads to different voltages being measured across the same circuit when a current is induced in the circuit. Includes an example problem.

Loops moving in uniform and non-uniform B-fields; induced EMF and Lenz's Law; Faraday's Law.

General proof of Faraday's Law; applications to dropped and levitating rings; relativity; connection to Maxwell's equations.

Creating EMF by changing area, angle, B; alternating current; changing magnitude of B.

Motivation; magnetic flux and Faraday's law stated; methods for inducing current; Lenz' Law; EMF of rod on conducting rails.

Induced electric fields, generators, and eddy currents.

Explanation of symmetry of electric and magnetic effects.

Strategies; rectangular loop near wire; area-changing loop; sliding rod; time-varying B-field; moving bars and loops.

Unworked problems: Concepts; sliding and rotating bars; RC circuit in time-varying B-field; AC generator; falling loop.

Three questions about Faraday's and Lenz's laws, with answers and explanations.

Five questions involving loops and rails in magnetic fields, with answers and explanations.

Why is current transformed to high voltage in power lines?

Solution (PDF)

Calculating induced EMF and voltmeter reading from a changing magnetic field.

Solution (PDF)

Finding induced EMF and current for a bar revolving around a circle of wire enclosing a magnetic field.

Solution (PDF)

Finding magnetic field strength inside air gap of square electromagnet.

Solution (PDF)

Finding maximum AC and power necessary to drive generator.

Solution (PDF)

Finding voltmeter readings and current in a circuit enclosing a changing magnetic field.

Solution (PDF)

Rod sits on rails in B-field; explaining motion of rod with current and without. Solution not included.

For loop descending through uniform field, finding dφ/dt, induced current, and velocity.

Solution (PDF)^#

A nail connects a circuit enclosing a charging solenoid; finding power, voltage, and current relationships for the nail.

Solution (PDF)^#

Video animation showing the induced current and magnetic field in a conducting ring that is falling in the magnetic field of a magnet.

Video animation showing the induced current and magnetic field in a conducting ring that is falling underneath the magnetic field of a magnet.

Video animation showing the induced current and magnetic field in a conducting ring that is falling past a magnet.

Video animation showing the induced current and magnetic field in a conducting ring that is falling past a magnet.

Video animations showing the magnetic field around a magnet that is falling towards a conducting ring.

Video animations showing the magnetic field around a magnet that is falling underneath a conducting ring.

Animated and live video showing the behavior of a magnet falling through a conducting ring.

Video animations showing the magnetic field and behavior of a magnet falling through a conducting ring with zero resistance.

Video animation showing the creating of a magnetic field by spinning up free charges in a series of five conducting rings.

Video animation showing the destruction of a magnetic field by slowing down the free charges in a series of five conducting rings.

Interactive applet showing the magnetic field and behavior of a ring falling towards a fixed magnet. The resistance of the ring and strength of the magnetic dipole moment can be varied to affect the behavior of the ring.

Interactive applet in which a conducting ring and a bar magnet can be moved toward or away from one another, leading to an induced current and magnetic field for the ring.

Interactive applet showing the induced current and magnetic field when the size and rotation of a conducting ring in a uniform magnetic field are changed.

Interactive applet showing the magnetic field and behavior of a magnet falling towards a conducting ring. The resistance of the ring and strength of the magnetic dipole moment can be varied to affect the behavior of the magnet as it falls.

Live video and animations showing the induced current in a conducting ring as a magnet is brought near it.

Live video and animation of a small magnet levitating above a superconducting disc.