Chapter 25

Electromagnetic Induction

Do Now (2/8/12): True or False1. Magnetic force is maximum when v and B are

perpendicular to each other.

2. A charge experiences magnetic force whether it is moving or not.

3. When the magnetic field is directed to the north while the positive charge is directed to the east, the magnetic force is directed into this paper.

4. When a proton and an electron are projected perpendicularly into a magnetic field, the electron will experience a larger magnetic force than the proton.

Review: Force on a single particle

•F = qvB

What is centripetal force?• Since the force is always perpendicular to

the velocity, it changes the particle's direction, but not its speed.

r

mvFc

2

Radius of Orbit• the particle travels in a circle such that:

r

mvqvB

FF cB

2

qB

mvr

Example:

•A proton orbits in a magnetic field of 0.2 T at 30 m/sec. What is the radius of its orbit?

Practice:

•Use the rest of class to work on the paper: Interaction between E and B matter

Do Now (2/9/12):

• A proton enters a magnetic field of 8.3 x 10-8 T with a speed of 7.5 x 107 m/s. What is the circumference of its circular path?

Mass spectrometer

• a device for accurately determining atomic mass.

• Atoms are ionized, accelerated to a known velocity, and curved in a B-field until they strike a photographic plate at P.

Mass spectrometer

• Charge to mass ratio

22

2

rB

V

m

q

Example:

• A beam of singly ionized oxygen atoms is sent through a mass spectrometer. The values are B=7.2x10-2T, r=0.085 m, and V=110 V. Find the mass of an oxygen atom.

E-Fields and B-Fields

B

Ev

FEqvB

FF eb

Example:

• A stream of singly ionized lithium atoms is not deflected at it passes through a B-field of 0.015 T that is perpendicular to an E-field of 650 N/C. What is the speed of the atom as it passes through the fields?

Do Now (2/10/12):

• A beam of doubly ionized oxygen atoms is sent through a magnetic field of 1.85 T in mass spectrometer. The radius of orbit is 0.95 m, and the voltage is 30 V. Find the mass of an oxygen atom.

Electromagnetic Induction

•The process of generating a current through a circuit by passing it through a magnetic field

Right-Hand Rule – same one!!!

•B = pointer finger

•F = middle finger

•v = thumb-motion

Electromotive Force

(EMF or ε)•Potential difference (V)

between two substances needed to

produce a current

THE TERM “ELECTROMOTIVE FORCE” CAN BE CONFUSING… BECAUSE IT IS NOT A FORCE AT ALL!!! IT IS A

VOLTAGE

REMINDER….

Electromotive Force•Produced when a length of wire is passed through

a magnetic field in a direction to the field

Electromotive Force•EMF = BLv

•B = magnetic field

•L = lengthwire in field

•v = velocitywire in field

Example:

A straight wire, 0.2 m long, moves at a constant speed of 7 m/s perpendicular to a magnetic field of 0.08 T.

1.What EMF is induced in the wire?

2.The wire has a resistance of 0.5 Ω. What is the current?

3.If a different metal (R=0.78Ω) were used for the wire what would the new current be?

Electromotive Force

•If the direction of the wire is not to the field, its component must be determined to determine

the EMF

Electromotive Force•EMF = BLvsinΘ

Practice:

• Use the rest of class to work on the paper Electromagnetic Induction. It is due on Tuesday!

Do Now (2/13/12):

A straight wire, 1.43 m long, moves at a constant speed of 9 m/s perpendicular to a magnetic field of 0.18 T.

1.What EMF is induced in the wire?

2.The wire has a resistance of 30 Ω. What is the current?

Magnetic Flux

cosBA

a measure of the number of magnetic field lines passing through an area. If a loop of wire with area A is in a field B, the flux is:

Measured in Webers (Wb)

Faraday’s Law

•Any change in a magnetic environment will cause a voltage (emf) to be "induced" in the coil.

Inducing EMF

• Changing area of coil

• Changing B-Field

• Changing B-flux

• Rotating coil (changing time)

Faraday’s Law

t

n

n = # of turns in coilΦ = fluxt = time

Example:

• http://farside.ph.utexas.edu/teaching/302l/lectures/node95.html

Do Now (2/14/12):A circular loop of wire of radius 40 cm which

has 25 turns is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of 60˚ with respect to the normal of the loop. The magnetic field strength is increased at a constant rate from 4T to 8T over 3 s.

1. What is the area of the loop?

2. What is the change in flux of the loop?

3. What is the EMF induced by the loop’s motion?

Pop quiz: A circular loop of wire (radius 0.3 m) which has

10 turns is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of 60˚ with respect to the normal of the loop. The magnetic field strength is increased at a constant rate from 5T to 10T over 6 s.

1. What is the area of the loop?

2. What is the change in flux of the loop?

3. What is the EMF induced by the loop’s motion?

Practice (2/14/12):

• Please use the rest of class to work on the paper “Faraday’s Law.” It is due tomorrow!!! Happy Valentine’s Day!!!!!!!!!!

Do Now (2/15/12):A circular loop of wire (radius 0.3 m) which has

10 turns is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of 60˚ with respect to the normal of the loop. The magnetic field strength is increased at a constant rate from 5T to 10T over 6 s.

1. What is the area of the loop?

2. What is the change in flux of the loop?

3. What is the EMF induced by the loop’s motion?

New Topic: Transformers!!!

2/15/12

Transformer• A transformer is composed of two different

coils of wire around opposite sides of an iron core.

• *passing current through wire that surrounds a metal core induces a magnetic field.

• This induced B-field will cause a responding current flow in a secondary coil wound around the opposite side.

Transformers

• Transformers are useful b/c if you change the number of turns from one side to the other, you change the voltage in the wire on the right! Transformers can change a high voltage to a lower one, or a low voltage to a higher one.

Step Up Transformers

• If you increase the number of turns on the right, the voltage coming off the transformer will increase in proportion.

Transformers• Transformers do not change POWER:

sspp

sp

IVIV

PP

Transformer Equation

• p=primary

• s=secondary

• N= # of turns

• V=voltage

• I=current

s

p

s

p

p

s

N

N

V

V

I

I

Example:

A step-up transformer has a primary coil consisting of 200 turns and a secondary coil consisting of 3000 turns. The primary coil is supplied with an effective AC voltage of 90 V.

1.What is the voltage in the secondary circuit?

2.If the current in the secondary coil is 2 A, what is the current in the primary circuit?

Practice (2/15/12):

•Please use the rest of class to work on the paper “Transformers.” It is due Friday!!!

Do Now (2/16/12):

• A step-down transformer has 7500 turns on its primary coil and 125 turns on its secondary coil. The voltage across the primary circuit 7.2 kV.

1.What voltage is being applied across the secondary circuit?

2.If the current in the secondary circuit is 36 A, what is the current in the primary circuit?

Practice (2/16/12):

•Please use the rest of class to work on the paper “Transformers.” It is due Friday!!!

Right-Hand Rule •B = fingers-MF

•F = up from palm

•v = thumb-motion