Unit 9: Part 2Electromagnetic Induction

and Waves

Outline

Induced emf: Faraday’s Law and Lenz’s Law

Electric Generators and Back emf

Transformers and Power Transmission

Electromagnetic Waves

Induced emf: Faraday’s Law and Lenz’s Law

We observe that, when a magnet is moved near a conducting loop, a current is induced. When the motion stops, the current stops.

Induced emf: Faraday’s Law and Lenz’s Law

On the other hand, when a loop moves parallel to a magnetic field, no current is induced.

Induced emf: Faraday’s Law and Lenz’s Law

We conclude that current is induced only when the magnetic field through the loop changes.

An induced emf is produced in a loop or complete circuit whenever the number of magnetic field lines passing through the plane of the loop or circuit changes.

Induced emf: Faraday’s Law and Lenz’s Law

Changing current in one loop can induce a current in a second loop.

Induced emf: Faraday’s Law and Lenz’s Law

In order to measure the change in the magnetic field through a loop, we define the magnetic flux:

SI unit of magnetic flux: the weber, Wb

Induced emf: Faraday’s Law and Lenz’s Law

Faraday’s law for the induced emf:

The minus sign indicates the direction of the induced emf, which is given by Lenz’s law.

Induced emf: Faraday’s Law and Lenz’s Law

Lenz’s law:

An induced emf in a wire loop or coil has a direction such that the current it creates produces its own magnetic field that opposes the change in magnetic flux through that loop or coil.

So if the magnetic field is increasing, the induced current will produce a field in the opposite direction, tending to decrease the field.

Induced emf: Faraday’s Law and Lenz’s Law

The direction of the induced current is given by a right-hand rule.With the thumb of the right hand pointing in the direction of the induced field, the fingers curl in the direction of the induced current.

Induced emf: Faraday’s Law and Lenz’s Law

Lenz’s law is a consequence of the conservation of energy.

Another way of viewing Lenz’s law is that the induced current is such that the flux through the loop tends to remain constant.

Electric Generators and Back emf

One way of changing the flux through a loop is to change its orientation with respect to the field. If this is done via some mechanical means, electricity can be generated.

Electric Generators and Back emf

The induced emf is then:

Such a generator is also called an alternator.

The emf as a function of time:

Electric Generators and Back emfIn common usage, we refer to the frequency rather than the angular frequency:

Electric Generators and Back emf

An electric motor has a loop rotating in a magnetic field, and will also create an induced emf.

This back emf is given by:

It limits the current in a motor and can help protect it.

Transformers and Power Transmission

A transformer can be used to reduce current while keeping power constant; this is useful in transmission lines, where losses depend on the current.

Since P = IV, reducing the current while the power remains unchanged means increasing the voltage.

Transformers and Power Transmission

A transformer works by induction—an ac current in the primary coil induces a current in the secondary coil. The voltage ratio depends on the number of loops in each coil.

Transformers and Power Transmission

The voltage ratio can be derived by looking at the induced emf.

Constant power means that

Therefore,

Transformers and Power Transmission

In reality, there is always some power loss between the primary and secondary coils, due to resistance, flux leakage, and self-induction.

Currents can also be induced in the bulk of the material itself; these are called eddy currents.

Transformers and Power Transmission

Eddy currents can function as powerful brakes for a solid conductor moving in a magnetic field. Braking can be reduced by shaping the conductor to make current loops difficult to form.

Electromagnetic Waves

James Clerk Maxwell showed how the electric and magnetic fields could be viewed as a single electromagnetic field, with the following properties:A time-varying magnetic field produces a time-varying electric field.A time-varying electric field produces a time-varying magnetic field.We have studied the first, but the second is new. We will not study it in detail, but will use its consequences.

Electromagnetic Waves

An accelerating charge produces an electromagnetic wave. The electric and magnetic fields are perpendicular to each other and to the direction of propagation of the wave.

Electromagnetic Waves

All electromagnetic waves travel at the same speed in vacuum:

In a vacuum, all electromagnetic waves, regardless of frequency or wavelength, travel at the same speed, c = 3.00 × 108 m/s.

This finite speed of electromagnetic waves leads to delays in transmitting signals over long distances, such as to spacecraft.

Electromagnetic Waves

An electromagnetic wave transmits energy; its electric and magnetic fields are capable of accelerating charged particles. It will exert a force on any surface it intercepts; this phenomenon is called radiation pressure. It is negligible in everyday experience, but could be used to power “solar sails” for interplanetary travel.

Electromagnetic WavesElectromagnetic waves can have any frequency. Different frequencies have been given different labels.

Electromagnetic Waves

Waves of different frequencies have different sources.

Review

Magnetic flux:

Faraday’s law of induction:

Lenz’s law: Induced emf tends to oppose the change that induced it.

AC generator:

Review

A transformer uses induction to reduce or increase current in a secondary coil.

An electromagnetic wave consists of time-varying electric and magnetic waves, perpendicular to each other and to the direction of propagation, and traveling with a speed of 3.00 × 108 m/s in vacuum.