Electromagnetic Induction

AP Physics 2

What is E/M Induction?

Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current.

Michael Faraday first discovered it, using some of the works of Hans Christian Oersted. His work started at first using different combinations of wires and magnetic strengths and currents, but it wasn't until he tried moving the wires that he got any success.

It turns out that electromagnetic induction is created by just that - the moving of a conductive substance through a magnetic field.

Magnetic Induction

As the magnet moves back and forth a current is said to be INDUCED in the wire.

Magnetic Flux

The first step to understanding the complex nature of electromagnetic induction is to understand the idea of magnetic flux.

Flux is a general term associated with a FIELD that is bound by a certain AREA. So MAGNETIC FLUX is any AREA that has a MAGNETIC FIELD passing through it.

A

B

We generally define an AREA vector as one that is perpendicular to the surface of the material. Therefore, you can see in the figure that the AREA vector and the Magnetic Field vector are PARALLEL. This then produces a DOT PRODUCT between the 2 variables that then define flux.

Magnetic Flux – The DOT product

How could we CHANGE the flux over a period of time?

• We could move the magnet away or towards (or the wire)
• We could increase or decrease the area
• We could ROTATE the wire along an axis that is PERPENDICULAR to the field thus changing the angle between the area and magnetic field vectors.

Faraday’s Law

Faraday learned that if you change any part of the flux over time you could induce a current in a conductor and thus create a source of EMF (voltage, potential difference). Since we are dealing with time here were a talking about the RATE of CHANGE of FLUX, which is called Faraday’s Law.

Example

A coil with 200 turns of wire is wrapped on an 18.0 cm square frame. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 2.0Ω . A uniform magnetic field is applied perpendicularly to the plane of the coil. If the field changes uniformly from 0 to 0.500 T in 0.80 s, find the magnitude of the induced emf in the coil while the field has changed as well as the magnitude of the induced current.

4.05 V

2.03 A

Why did you find the ABSOLUTE VALUE of the EMF?

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What happened to the “ – “ that was there originally?

Lenz’s Law

Lenz's law gives the direction of the induced emf and current resulting from electromagnetic induction. The law provides a physical interpretation of the choice of sign in Faraday's law of induction, indicating that the induced emf and the change in flux have opposite signs.

Lenz’s Law

In the figure above, we see that the direction of the current changes. Lenz’s Law helps us determine the DIRECTION of that current.

Lenz’s Law & Faraday’s Law

Let’s consider a magnet with it’s north pole moving TOWARDS a conducting loop.

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DOES THE FLUX CHANGE?

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DOES THE FLUX INCREASE OR DECREASE?

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WHAT SIGN DOES THE “Δ” GIVE YOU IN FARADAY’S LAW?

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DOES LENZ’S LAW CANCEL OUT?

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What does this mean?

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Yes!

Increase

Positive

NO

This means that the INDUCED MAGNETIC FIELD around the WIRE caused by the moving magnet OPPOSES the original magnetic field. Since the original B field is downward, the induced field is upward! We then use the curling right hand rule to determine the direction of the current. (This is similar to an action-reaction force pair)

B_induced

Lenz’s Law

A magnet is dropped down a conducting tube.

The magnet INDUCES a current above and below the magnet as it moves.

The INDUCED current creates an INDUCED magnetic field of its own inside the conductor that opposes the original magnetic field.

Since the induced field opposes the direction of the original it attracts the magnet upward slowing the motion caused by gravity downward.

If the motion of the magnet were NOT slowed this would violate conservation of energy!

Lenz’s Law

Let’s consider a magnet with it’s north pole moving AWAY from a conducting loop.

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DOES THE FLUX CHANGE?

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DOES THE FLUX INCREASE OR DECREASE?

​

WHAT SIGN DOES THE “Δ” GIVE YOU IN FARADAY’S LAW?

​

DOES LENZ’S LAW CANCEL OUT?

​

What does this mean?

​

Yes!

Decreases

negative

yes

In this case, the induced field DOES NOT oppose the original and points in the same direction. Once again use your curled right hand rule to determine the DIRECTION of the current.

B_induced

In summary

Faraday’s Law is basically used to find the MAGNITUDE of the induced EMF. The magnitude of the current can then be found using Ohm’s Law provided we know the conductor’s resistance.

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Lenz’s Law is part of Faraday’s Law and can help you determine the direction of the current provided you know HOW the flux is changing

Motional EMF – The Rail Gun

A railgun consists of two parallel metal rails (hence the name) connected to an electrical power supply. When a conductive projectile is inserted between the rails (from the end connected to the power supply), it completes the circuit. Electrons flow from the negative terminal of the power supply up the negative rail, across the projectile, and down the positive rail, back to the power supply.

In accordance with the right-hand rule, the magnetic field circulates around each conductor. Since the current is in opposite direction along each rail, the net magnetic field between the rails (B) is directed vertically. In combination with the current (I) across the projectile, this produces a magnetic force which accelerates the projectile along the rails. There are also forces acting on the rails attempting to push them apart, but since the rails are firmly mounted, they cannot move. The projectile slides up the rails away from the end with the power supply.

Motional Emf

There are many situations where motional EMF can occur that are different from the rail gun. Suppose a bar of length, L, is pulled to right at a speed, v, in a magnetic field, B, directed into the page. The conducting rod itself completes a circuit across a set of parallel conducting rails with a resistor mounted between them.

Motional EMF

In the figure, we are applying a force this time to the rod. Due to Lenz’s Law the magnetic force opposes the applied force. Since we know that the magnetic force acts to the left and the magnetic field acts into the page, we can use the RHR to determine the direction of the current around the loop and the resistor.

Example

An airplane with a wing span of 30.0 m flies parallel to the Earth’s surface at a location where the downward component of the Earth’s magnetic field is 0.60 x10^-4 T. Find the difference in potential between the wing tips is the speed of the plane is 250 m/s.

0.45 V

In 1996, NASA conducted an experiment with a 20,000-meter conducting tether. When the tether was fully deployed during this test, the orbiting tether generated a potential of 3,500 volts. This conducting single-line tether was severed after five hours of deployment. It is believed that the failure was caused by an electric arc generated by the conductive tether's movement through the Earth's magnetic field.

Generators

AC Generators use Faraday’s law to produce rotation and thus convert electrical and magnetic energy into rotational kinetic energy. This idea can be used to run all kinds of motors. Since the current in the coil is AC, it is turning on and off thus creating a CHANGING magnetic field of its own. Its own magnetic field interferes with the shown magnetic field to produce rotation.

Figure 23.20

• When this generator coil is rotated through one-fourth of a revolution, the magnetic flux Φ changes from its maximum to zero, inducing an emf.

Generators

A generator with a single rectangular coil rotated at constant angular velocity in a uniform magnetic field produces an emf that varies sinusoidally in time. Note the generator is similar to a motor, except the shaft is rotated to produce a current rather than the other way around.

Generators

emf = ω NBA sin ωt

Figure 23.22

Back EMF

The current in the rotating coil is limited by the back emf.

The term back emf is commonly used to indicate an emf that tends to reduce the supplied current.

The induced emf explains why the power requirements for starting a motor and for running it are greater for heavy loads than for light ones.

The coil of a DC motor is represented as a resistor in this schematic. The back emf is represented as a variable emf that opposes the one driving the motor. Back emf is zero when the motor is not turning, and it increases proportionally to the motor’s angular velocity.

Transformers

Probably one of the greatest inventions of all time is the transformer. AC Current from the primary coil moves quickly BACK and FORTH (thus the idea of changing!) across the secondary coil. The moving magnetic field caused by the changing field (flux) induces a current in the secondary coil.

If the secondary coil has MORE turns than the primary you can step up the voltage and runs devices that would normally need MORE voltage than what you have coming in. We call this a STEP UP transformer.

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We can use this idea in reverse as well to create a STEP DOWN transformer.

Transformers

The plug-in transformer has become increasingly familiar with the proliferation of electronic devices that operate on voltages other than common 120 V AC. Most are in the 3 to 12 V range. (credit: Shop Xtreme)

Transformers

Transformers change voltages at several points in a power distribution system. Electric power is usually generated at greater than 10 kV, and transmitted long distances at voltages over 200 kV—sometimes as great as 700 kV—to limit energy losses. Local power distribution to neighborhoods or industries goes through a substation and is sent short distances at voltages ranging from 5 to 13 kV. This is reduced to 120, 240, or 480 V for safety at the individual user site..

Transformers

A typical construction of a simple transformer has two coils wound on a ferromagnetic core that is laminated to minimize eddy currents. The magnetic field created by the primary is mostly confined to and increased by the core, which transmits it to the secondary coil. Any change in current in the primary induces a current in the secondary.

Transformers

Transformers

http://alan-parekh.com/wp-content/uploads/2010/11/12_volt_plug_in_power_supply.jpg

1,500 Wraps

500 Wraps

30 Volts OUT

10 Volts IN

1,000 Wraps

20 Volts OUT

50 Volts OUT

Transformers

Power IN = Power OUT�V∙I = V∙I

P = V · I�Power = Voltage · Current

12.0�Volts

400 wraps

100 wraps

?�Volts

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Primary�Coil

Secondary�Coil

http://www.powerstream.com/Wire_Size.htm

V = I∙R

120 = 2.7∙R

R = 44.4 Ω

Length = 1370 ft

Don’t leave these transformers plugged in!�It wastes energy!

http://static.howstuffworks.com/gif/transformer2.jpg

Power_loss = I² ∙ R

= 2.7² ∙ 44.4

= 324 Watts

= 64 Watts

= .53² ∙ 226 Ω

Power = I² ∙ R

V = I ∙ R

120 = I ∙ 169.1

I = .709 Amps

Power = .709² ∙ 169.1

Power = 85.2 Watts

http://www.meppi.com/Products/Transformers/PublishingImages/DSC_0035.JPG

120,000 Volts

P = V · I�Power = Voltage · Current

http://www.mission10x.com/mission-10x/Documents/Electric_transmission_lines.jpg

P = I² · R�Power = Current² · Resistance

�Power_Delivered = Power_Produced – Power_Lost�

Power_Delivered = V · I – I² · R

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10,000 Volts

120 Volts

http://www.mission10x.com/mission-10x/Documents/Electric_transmission_lines.jpg

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