Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Electromagnetic Induction and Faraday’s Law
Sections 21.3 - 21.5
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Reading Assignment
Read sections 21.7 - 21.10
Homework Assignment 6
Homework for Chapter 21 (due at the beginning of class on Friday, October 8)
Q: 4, 6, 15, 18
P: 8, 12, 18, 30, 44, 72
PP: 29.3
2010 Smith Lecture
Lawrence Krauss will deliver “Einstein’s Biggest Blunder: A Cosmic Mystery Story” on Wednesday,
October 6 at 7:30 pm in the Duke Family Performance Hall
Free and open to the public
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Faraday’s Law
The induced electromotive force (emf) ε in any closed circuit is equal to the time rate of change of the
magnetic flux through the circuit
∆ΦB
ε=−
∆t
If a coil consists of N loops with the same area, and ΦB is the magnetic flux through one loop, then the
total induced emf in the coil is
∆ΦB
ε = −N
∆t
Lenz’s law
An induced current has a direction such that the magnetic field due to the induced current opposes the change in
the magnetic flux that induced it
The minus sign
Lenz’s law gives us a physical interpretation for the minus sign in Faraday’s law
Conclusion
A changing magnetic field produces an electric field
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Eddy currents
An emf and a current are induced in a circuit by a changing magnetic flux
Circulating currents (eddy currents) are induced in bulk conductors moving through a magnetic field
The direction of these currents is such that they create magnetic fields that oppose the change that caused
the current (Lenzs law)
These currents can result in repulsive or drag forces between the conductor and the external magnet
The braking system of many subway and rapid-transit cars make sure of electromagnet induction and eddy
currents
Reducing Eddy currents
Eddy currents are often undesirable because they represent a transformation of mechanical energy to
internal energy
To reduce this energy loss, conducting parts are often laminated; that is, they are built up in thin layers
separated by a nonconducting material such as lacquer or a metal oxide
This layered structure prevents large current loops and effectively confines the currents to small loops in
individual layers
Such a laminated structure is used in motors to minimize eddy currents and thereby increase its efficiency
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through
Electromagnetic Induction and Faraday’s Law
Final Questions
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through
AC and one coil of wire
To help us understand how power transfer takes place in a transformer, let’s start with a simple question:
what happens when you send AC through a single coil of wire?
Because currents are magnetic, the coil becomes an electromagnet
However, since the current passing through reverses periodically, so does its magnetic field
This alternating magnetic field produces an alternating electric field
This electric field pushes on the very alternating current that produced it
As the coil’s current increases, the induced electric field pushes that current backward and opposes
its increase
As the coil’s current decreases, the induced electric field pushes that current forward and opposes
its decrease
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Transformers
A transformer is a device that transfers electrical energy from one circuit to another through
AC and one coil of wire
To help us understand how power transfer takes place in a transformer, let’s start with a simple question:
what happens when you send AC through a single coil of wire?
Because currents are magnetic, the coil becomes an electromagnet
However, since the current passing through reverses periodically, so does its magnetic field
This alternating magnetic field produces an alternating electric field
This electric field pushes on the very alternating current that produced it
As the coil’s current increases, the induced electric field pushes that current backward and opposes
its increase
As the coil’s current decreases, the induced electric field pushes that current forward and opposes
its decrease
AC and two coils of wire
In a single coil, energy that’s transferred from the current to the magnetic field must eventually return to
the current (it has nowhere else to go!)
But, if there were two coils and two currents, energy transferred from one current to the magnetic field can
move on to the second current!
A transformer is a device that uses magnetic fields to transfer electric power from one circuit to another
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
An AC transformer
For simplicity, we will imagine that an AC transformer consists of two coils of wire, wound around an iron
core
The primary winding consists of N1 turns and is connected to the alternating voltage source
The voltage across the primary is
∆V1 = −N1
dΦB
dt
The secondary winding consists of N2 turns
The voltage across the secondary is
∆V2 = −N2
dΦB
dt
Therefore, a current I2 is induced in the secondary!
In general, the output voltage differs from the input voltage
∆V2
∆V1
=
N2
N1
If N2 > N1 , the output voltage ∆V2 exceeds the input voltage ∆V1 (a step-up transformer)
If N2 < N1 , the output voltage ∆V2 is less than the input voltage ∆V1 (a step-down transformer)
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Conclusions
Alternating current is used to deliver electricity to businesses and residences
For economical concerns, small currents are transported at large voltages (P = I ∆V )
However, large voltages are dangerous inside the home (sparks fly!)
Transformers are used to transfer the incoming electricity from large voltages to safer smaller voltages
inside the home, without power loss
Transformers work by magnetic induction (Faraday’s law)
They will not work if you use a direct current power source
Electromagnetic Induction and Faraday’s Law
Announcements
Faraday’s Law
Eddy Currents
AC Transformer
Final Questions
Reading Assignment
Read sections 21.7 - 21.10
Homework Assignment 6
Homework for Chapter 21 (due at the beginning of class on Friday, October 8)
Q: 4, 6, 15, 18
P: 8, 12, 18, 30, 44, 72
PP: 29.3
2010 Smith Lecture
Lawrence Krauss will deliver “Einstein’s Biggest Blunder: A Cosmic Mystery Story” on Wednesday,
October 6 at 7:30 pm in the Duke Family Performance Hall
Free and open to the public
Electromagnetic Induction and Faraday’s Law