Electromagnetic Induction

Electromagnetic Induction

Unit 6

Where We Are

• We will be covering four lessons in this unit.

• This material will not be on Friday’s test.

• However, there will be a ~20-30 min quiz on this material next Wednesday.

Where We Are

• In the last unit, we saw two ways in which electricity and magnetism are related:– Electric currents produce magnetic fields.– Magnetic fields exert forces on electric

currents.

• Scientists began to wonder if magnetic fields could produce electric currents.

Faraday and Induced EMFs

• Michael Faraday conducted a series of experiments to see if he could use a magnet to produce a current.

• A coil of wire was connected to a battery.


• The current through coil x produced a magnetic field, which was amplified by the iron core.

• A second coil, Y, was hooked up to a galvanometer, which would detect even a small current, but not to a battery.


• Faraday hoped that a strong, steady current through coil X would produce a current in coil Y.

• However, no current was observed, even when a very strong current was used.


• However, Faraday noticed that the galvanometer jumped when at the moment he closed the switch in circuit X.

• The needle jumped in the opposite direction at the moment opened the switch.


• A constant current in X produced no current in Y.

• Only when the current in X was starting or stopping was a current observed in Y.


• As the current is turning on or off, the magnetic field generated by X is changing.

• When the B field was changing, an induced current was observed in Y


• Since current arises when there is an EMF (like a battery) in the circuit, Faraday concluded:

• WARNING: Steady B fields do nothing. Only changing B fields produce EMFs.

A changing magnetic field induces an EMF.


• This phenomenon is called electromagnetic induction.

• Faraday went on to do further experiments with this phenomenon.


• Faraday showed that if a magnet is moved quickly into a coil of wire, a current is induced.

• If the magnet is removed, a current is induced in the opposite direction.


• Faraday also showed that the same effect occurs if the magnet is held steady and the coil of wire is moved.

• Motion or change is required to induce an EMF, but it is only relative motion that counts.

COOL VIDEO

http://www.youtube.com/watch?v=stUDqGzpev8

Magnetic Flux

• As Faraday began quantitative investigations of these effects, he discovered the strength of the EMF did not just depend on how fast B was changing.

• It also depended on the area enclosed by the loop of wire, and the angle between the wire and the B field.

Magnetic Flux

• These effects are unified in the concept of magnetic flux.

• Magnetic flux is a measure of the number of magnetic field lines that pass through a surface with a given area.

Magnetic Flux

• Magnetic flux is denoted B, and is calculated using the formula

Magnitude of the B field

Area of the surface

Angle between B a line

perpendicular to A

Magnetic Flux

• These effects are unified in the concept of magnetic flux.

• Magnetic flux is a measure of the number of magnetic field lines that pass through a surface with a given area.

Magnetic Flux

• Notice that the magnetic flux is greatest when the magnetic field is perpendicular to the surface.

• Magnetic flux is measured in webers.

Conceptual Example: Magnetic Flux

A square loop of wire encloses an area A1 as shown. Inside the wire is a region of uniform magnetic field, B, perpendicular to the loop. The B field extends over area A2. What is the magnetic flux through the loop of wire?

Example: Magnetic FluxA square loop of wire is in a 1.25 T magnetic field. If the length of each side of the loop is 10 cm,

a) What are the maximum and minimum values for the magnetic flux through the loop?

b) What is the flux when the angle between B and the line perpendicular to A is 35º?

Homework

• Read sections 21-1 and 21-2.

• Do problem 7 on page 610.

Faraday’s Law of Induction


• Faraday determined the induced EMF depended on a change in the B field.

• It also depended on the area of the loop of wire, and the angle the loop was placed at.

• All of these items are represented in the concept of magnetic flux developed yesterday.


• Faraday concluded at a change in magnetic flux over a time interval t will induce an EMF in a loop of wire.

• Mathematically, this is represented by

• We will talk about the minus sign in a moment.


• If the wire has multiple coils, the EMF is multiplied by the number of coils. So

• Here, N is the number of coils in the wire loop.

• This is Faraday’s Law of Induction.

Example: Faraday’s LawA square coil of wire (sides of length 5 cm) is initially in a 0.6 T magnetic field as shown. It is quickly pulled out of the field to a region where B = 0. If it takes 0.1 s for the entire coil to leave the field, what EMF is induced in the coil?

Lenz’s Law

Lenz’s Law

• You have already noticed the odd minus sign in Faraday’s Law.

• You might also have noticed that we did not specify a direction for the current in the last example.

• Both of these are explained by Lenz’s Law.

Lenz’s Law

• Lenz’s Law states

• Be careful here: we are now talking about two separate magnetic fields. – The magnetic field generating the change

in flux.– The magnetic field produced by the

induced current.

The current produced by an induced EMF moves in a direction so that its magnetic field opposes the original change in flux.

Lenz’s Law

• Here’s a helpful way to think about Lenz’s Law:– When the flux through a loop changes, magnetic

field line are either being “lost” or “gained.”

– If flux goes down and lines are “lost” the current moves to generate a B field to “replace” those lost lines.

– If the flux goes up and lines are “gained” the current moves to generate a B field pointing in the opposite direction to “cancel out” those new lines.

Conceptual Example

Conceptual Example

Example: Faraday’s LawLet’s revisit the last example:

a) What direction is the current flowing?

b) How much current is flowing?

c) If the coil has a resistance of 100 , how much energy is dissipated in the coil in the 0.1 s of motion?

Homework

• Do problems 1, 2, and 7 on page 610.

Problem Day

• Do problems 4, 5, 9, and 10 on page 610.

Homework

• Read sections 21-3 and 21-4.

• Do problems 11 and 13 on page 611.

EMF in a Moving Conductor

EMF on a Moving Conductor

• Suppose we have the following setup:

• A conducting rod is moving with speed v as shown.


• Lenz’s Law tells us that this will create a current that flows in a direction that opposes the change in flux.

• We want to quantify the EMF through Faraday’s Law.


• As the rod moves, the size of the loop is increased.

• This means the magnetic flux through the loop is increasing.


• Faraday’s Law tells us that the EMF is found by


• So, the change in flux is


• To find the change in area, notice that the rod travels a distance

in the time t.

EMF on a Moving Conductor• This means the change in area is

• And the change in flux is


• Plugging this into Faraday’s Law


• Plugging this into Faraday’s Law

Example: Airplane

An airplane is traveling at 1000 km/hr. If the Earth’s magnetic field is 5 x 10-5 T and points vertically. If the wingspan of the plane is 70 m, what is the EMF induced in the wings of the plane?

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Electromagnetic Induction