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AP C UNIT 11 ELECTROMAGNETIC INDUCTION

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AP C UNIT 11 ELECTROMAGNETIC INDUCTION. Recall Electric Flux. Welcome our newest concept… Magnetic Flux. Faraday’s Observations,1830. When a magnet moves toward a loop of wire, the ammeter shows the presence of a current - PowerPoint PPT Presentation

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Page 1: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

AP C UNIT 11 ELECTROMAGNETIC

INDUCTION

Page 2: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Recall Electric Flux

cosEAE

Page 3: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Welcome our newest concept… Magnetic Flux

Page 4: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Faraday’s Observations,1830• When a magnet moves

toward a loop of wire, the ammeter shows the presence of a current

• When the magnet is held stationary, there is no current

• When the magnet moves away from the loop, the ammeter shows a current in the opposite direction (c)

• If the loop is moved instead of the magnet, a current is also detected

Page 5: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Experimental Conclusions

• A current is set up in the circuit as long as there is relative motion between the magnet and the loop– The same experimental results are found whether the

loop moves or the magnet moves

• The current is called an induced current since there is no power source.

• An EMF is actually induced by a change in the magnetic flux.

Page 6: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Faraday’s Law & Electromagnetic Induction

• The instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuit.

EM induction refers to electricity deriving from magnetism whereas electromagnetism is the opposite.

Page 7: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Traffic light sensors

There is an inductive loop at intersection of Ft Wash & Susquehanna.

Page 8: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Electric Guitar• A vibrating string induces

an emf in a coil• A permanent magnet

inside the coil magnetizes a portion of the string nearest the coil

• As the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coil

• The changing flux produces an induced emf that is fed to an amplifier

Page 9: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Apnea Monitor

• The coil of wire attached to the chest carries an alternating current

• An induced emf produced by the varying field passes through a pick up coil

• When breathing stops, the pattern of induced voltages stabilizes and external monitors sound an alert

Page 10: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Applications of Faraday’s Law – Ground Fault Interrupters

• The ground fault interrupter (GFI) is a safety device that protects against electrical shock– Wire 1 leads from the wall outlet to

the appliance– Wire 2 leads from the appliance

back to the wall outlet– The iron ring confines the magnetic

field, which is generally 0– If a leakage occurs, the field

is no longer 0 and the induced voltage triggers a circuit breaker shutting off the current

Page 11: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

• Faraday's Law is the basic principle behind the microphone. In a microphone there is a diaphragm, around which a coil is wrapped, which can move back and forth in response to sound waves. A stationary bar magnet, placed near the coil, induces current in the coil which can then be transmitted (with amplification) to the speaker.

Page 12: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

A long wire carries current i a distance ‘d’ from a rectangular wire loop as shown above. Determine an expression for the flux through loop.

i

w

l

d

Example

Page 13: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Suppose that i(t) = 3t +1. Find induced voltage in loop

Page 14: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Negative sign explained in Faraday’s Law

The negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law:

Page 15: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

i

w

l

d

If i(t) = 3t +1, what was direction of induced current in loop as t increases?

Page 16: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Lenz’s Law examples

Determine direction of induced current in loop

Page 17: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Determine direction of induced current in loop as magnet approaches loop area.

Page 18: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Determine direction of induced current in loop as loop gets smaller.

Page 19: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

When switch is closed, describe current flow in R

IRON CORE

Page 20: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Describe current through R when I goes to zero.

Page 21: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Which situation(s) cause(s) induced current?

Page 22: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Example

(a) ccw (b) cw (c) no induced current

What is the direction of the induced current in the loop?

A conducting rectangular loop moves with constant velocity v in the -y direction and a constant current I flows in the +x direction as shown x

v

Iy

Iinduced

Page 23: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

GeneratorA coil of wire turns in a magnetic field. The flux in the coil is constantly changing, generating an emf in the coil.

Converts mechanical energy to electrical energy

Page 24: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

If loop is made to rotate at constant rate ω in uniform B, we have from Faraday’s Law:

Page 25: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

(e)Motional EMF

• A straight conductor of length ℓ moves perpendicularly with constant velocity through a uniform field

ℓℓ

Page 26: AP C UNIT 11 ELECTROMAGNETIC INDUCTION
Page 27: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

A conducting bar is placed across conducting path and pulled to right with speed v as shown.

As bar moves, a change in flux occurs which induces CCW current.

Page 28: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Also, a magnetic force on bar arises which acts as a resistance to the motion of the bar as it is pulled to the right

Page 29: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Lenz’ Law Revisited, Conservation of Energy Consequence• Assume the induced current is

clockwise instead…– The magnetic force on the bar

would be to the right– The force would cause an

acceleration and the velocity would increase

– This would cause the flux to increase and the current to increase and the velocity to increase…

This would violate Conservation of Energy and so therefore, the current must be counterclockwise

Page 30: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

exampleA metal rod of mass 0.22kg lies across two parallel conducting rails which sits on a tabletop as shown. The rod and rails have negligible resistance but significant friction where uk=0.20. A field of 0.80T points into page. A string pulls the rod to right at a constant speed of 1.8m/s.

Page 31: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

a) Calculate the force needed to pull rod at constant speed.

b) Calculate the energy dissipated in the resistor in 2.0s.

c) Calculate the work done by string in 2.0s.

Page 32: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

ExampleA conducting rod with mass m and length L moves on two frictionless parallel rails in the presence of a uniform magnetic field. The bar is given an initial velocity vi at time t=0. Calculate the velocity of the bar as a function of time. Bar will slow down due to resistive force.

Page 33: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

The magnitude of the magnetic force is given by

Now, using Newton's second law, we can write the net force on the conducting rod as

Page 34: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Eddy currentsEddy currents are small circular or swirling currents that arise in conductors like a sheet of metal.

Page 35: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Eddy currents lead to heat being generated in the conductor

This is the basic principle behind induction stoves. Safe to touch unless you are metallic. Eddy currents are established in cookware causing metal to heat up.

Page 36: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Magnetic Braking

Analog speedometers

Rollercoaster brakes

Page 37: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

The Lamar Advantage 4200 Elliptical Trainer by Star Trac will allow you to train smarter by delivering an effective full-body workout without the joint pounding stress associated with jogging. As you exercise, contoured urethane rollers glide smoothly on our dual-rail tracking system. By offering 16 intensity levels, the electronically controlled magnetic brake (ECB) will continue to provide a challenge.

Elliptical Machines

Page 38: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Metal Detectors

Page 39: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Transformers

A transformer is a device used to change the voltage in a circuit. AC currents must be used.

75,000 V in the power lines

120 V in your house

Page 40: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Electrical Power Transmission• When transmitting electric power over long distances,

it is most economical to use high voltage and low current, which minimizes I2R power losses.

Page 41: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Ampere's Law has shown us how currents, moving electric charges, can create magnetic fields.

Faraday's Law has shown us how changing magnetic fields can induce an emf in a closed loop.

Induced E-fields

Page 42: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Consider a loop of wire outside of a solenoid. Current is flowing through solenoid from back to front where B-field from coils is into page.

Side View Front View

Page 43: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

If the current is dereased gradually, the magnetic field in the solenoid's core decreases and an emf & Iinduced will be induced in the wire loop (LENZ LAW).

Page 44: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

The force that pushes the charges around the wire is F = qE, where E is the induced electric field.

Page 45: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

E-fields produced by either static charge or induction both exert forces on charged particles, however, there is an important difference.

Static E Induced E

Page 46: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

b

a

ab dEV Recall we previously learned that

the potential difference between 2 points in a static field is given by:

Page 47: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

However, in a changing B-field case…

As charge makes journey around closed loop, it must be experiencing an emf, however, to interpret that as a changing potential, it doesn’t make sense. Why?

Page 48: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

As magnetic field increases in time through loop, an electric field is generated

timeB

Page 49: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Consider B-field between pole of electromagnet. Assume B to be uniform at any instant over a circular radius R. The current in the windings of the electromagnet increase with time. Beyond the circular region (r > R), assume B=0. Find E at any distance r from the center.

S

N

side view top view, looking down on N pole

Page 50: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

r r

E

E

Page 51: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Use my college physics text to redo next slides…do RL circuit, then do energy…p904

Inductance is typified by the behavior of a coil of wire in resisting any change of electric current through the coil.

Page 52: AP C UNIT 11 ELECTROMAGNETIC INDUCTION
Page 53: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

InductanceSimilar to the idea of capacitance (holding onto charge), inductance deals with how well an inductor holds onto a magnetic field.

Page 54: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Energy Density of solenoid

Page 55: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Close switch

As soon as current appears at the first coil of the inductor, a change in magnetic flux is created, and therefore an EMF. This EMF pushes opposite to the EMF causing the flux in the first place, according to Lenz's Law

RL CIRCUIT

Page 56: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

We expect that the current in the inductor, and hence in the entire circuit, must increase over time until it reaches its maximum value of imax = ε / R where ε is the voltage provided by the EMF source. Resistance of inductor goes to zero whereas in capacitor we say it becomes infinite R.

Page 57: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

di/dt is positive since current is increasing, however, the EMF induced across the inductor is negative since it is pushing current in opposite direction to oppose change, therefore a minus sign is added

Going CW around circuit:

Page 58: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Current versus time in an R-L circuit

63%Imax

Page 59: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Flipping switch back causes decrease in current. Similar analysis yields:

37%Imax

Page 60: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Example: Close S1. After a long time:

a) Find value of current in inductor at moment S1 is closed.

b) Find value of current in inductor after long time.

Simultaneously open S1 and close S2.

At that moment, what is current in inductor?

Find current at t=2.0x10-3s in inductor.

20V

100Ω 0.10H

Page 61: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Example 240V

2.2H160Ω

Determine the work done by the battery from t = 0s to 0.0165s.

Page 62: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

LC CircuitsAnalogous to an oscillating mass on a spring

Page 63: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

The Oscillation Cycle

Prior to discharge, all energy resides in E-field of capacitor. When capacitor discharges, current flows CW and gets larger, B-field emerges in inductor resisting change.

At t=T/4, capacitor has zero charge, current has max value, B-field is max with all energy now residing in inductor’s field.

Page 64: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Eventually charge starts to accumulate on capacitor, current dies, B-field decreases to zero. At t=T/2, all energy is back in E-field with polarity of capacitor reversed.

Process repeats itself returning to state it was at t = T/4. At t = 3T/4 energy is back in B-field. This is called electrical oscillation.

Page 65: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

LC Circuit Analysis:

Page 66: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

What differentiates an LC circuit from the RC or RL circuit is the fact that current in both the RC and RL circuits changes exponentially towards a steady state.However, in the LC circuit, the current oscillates, never reaching steady state.

L C Circuit Analogy to SHM

Page 67: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Current and Charge variations with time for LC circuit

System oscillates according to:

Just like resonance in SHM, LC circuit has electrical resonance. Your radio is tuned in to a resonant frequency by changing the capacitance

Page 68: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Maxwell’s EquationsWe now gather all of the governing equations together

Maxwell retooled Ampere’s law which is only good for static case, not oscillating situations

The net magnetic flux is zero through a closed surface. B field lines cannot begin or end at any point. If they did, monopoles would exist

Page 69: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

These four equations describe all of classical electric and magnetic phenomena

Maxwell’s Equations

Page 70: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

Maxwell’s own contribution is just the last term of the last equation but realizing the necessity of that term had dramatic consequences.  It made evident for the first time that varying electric and magnetic fields could feed off each other & these fields could propagate indefinitely through space, far from the varying charges and currents where they originated.  Previously, the fields had been envisioned as tethered to the charges and currents giving rise to them.   Maxwell’s new term (he called it the displacement current) freed them to move through space in a self-sustaining fashion, and even predicted their velocity it was the velocity of light!

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Page 72: AP C UNIT 11 ELECTROMAGNETIC INDUCTION

As the E-field starts to change, that in turn induces a B-field which in turns induces E and so on.