Induction Consider a conductor moving in a magnetic field…. X X X X X.

Induction

Consider a conductor moving in a magnetic field….

X X X X X

X X X X X

X X X X X

X X X X X

The conductor is filled with mobile charges (by definition).

X X X X X

X X X X X

X X X X X

X X X X X

+ +++

This causes, (induces) a current to flow.

Each charge is a moving charge in a magnetic field, and will therefore have a force exerted on it. (RHR#3)

The conductor is filled with mobile charges (by definition).

X X X X X

X X X X X

X X X X X

X X X X X

+ +++

We call this phenomena

Electromagnetic Induction

An electromotive force (emf) is produced in a conductor whenever it cuts across magnetic field lines. No emf

arises from motion parallel to a magnetic field.

Coil moves Down

Coil moves Up

Magnetic Field Lines

Calculating EMF

EMF = Electromotive Force (Volts)B = Magnetic Field (T)L = Length of the wire (m)v = velocity of wire that is moving in the field (m/s) = angle between wire and magnetic field

Lenz’s Law:The direction of an induced current is

always such that its own magnetic field opposes the magnetic field responsible for producing it.

Lenz’s law is a statement of the Law of Conservation of Energy

Drop a magnet through a conducting ring.

N

SA current will be

induced in the ring.

Consider a charge Q in

the ring

Drop a magnetic through a conducting ring.

N

SThe

secondary magnetic

lines of force always

oppose the creating lines

of force.

N

S

pull

As the loop is pulled out of the field, a current will be induced

in the loop.

N

S

pull

Consider the force on this leg of the loop

Induced force opposes original

force

• Usually it isn’t a single straight wire that is moving in a external magnetic field.

• Usually it is a coil of wires (like what you saw with the motor) that are rotating in the magnetic field.

Alternating Current (AC)

Remember, a coil is just a solenoid with one loop & a solenoid creates a magnetic field just

like a magnet

B

BBB

BDRAW

THIS

Alternating Current (AC)• This is how the electric

company generates the electricity we use.

• Mechanical energy (spinning the coil) turns into electrical energy (EMF)

• The catch is figuring out what will spin the coil in the external magnetic field.

Effective Current & Effective VoltageUnits: Amps

Ieff = effective current (average current)

Imax = maximum current

Units: VoltsVeff = effective voltage

(average voltage)Vmax = maximum voltage

In the USA, Veff = 120 V

Example: A generator is created by moving a 0.20 m long wire in an external magnetic field of 2.0 T at a speed of 15 m/s. (A) What EMF is produced by the generator?

EMF = (2.0 T)(0.20 m)(15 m/s)sin90o

EMF = 6.0 V

(B) If the 6.0V is the maximum voltage produced by the generator, what is the effective emf?

Veff = 0.707 (6.0 V)

Veff = 4.2 V

(C) If the generator is hooked up to a light bulb with a resistance of 2.5 , what is

the effective power of the the bulb?

Remember: P = IV = I2R = V2/R

Peff = (Veff)2/R

Peff = (4.2)2/2.5

Peff = 7.1 W

Mutual Inductance• Mutual inductance is a measure of the

ability of one circuit carrying a changing current to induce an emf in a nearby circuit.

• The coil carrying the current initially is called the primary coil.

• The coil in which the current is induced is called the secondary coil.

Transformers

• Transformers are devices that change one AC potential difference to a different AC potential difference.

• Real transformers are not perfectly efficient.– Efficiencies of real transformers typically range

from 90% to 99%.

• For this class, we will assume 100% efficiency. (We like living in an ideal world) :)

Residential Power Poles usually have 3 levels of wires.

High Voltage

120 –240 Volts

Telephone-Cable TV

Transformer

There are two types of transformers:

1. Step up and2. Step down

Step up vs Step down:Think of a staircase

• Step up: Start with a low voltage, end with a higher voltage

• Step down: Start with a high voltage, end with a lower one.

Vp

Vp

Vs

Vs

Transformerscoilssecondary

voltssecondary

coilsprimary

voltsprimary

##

Volts x amps = Volts x amps

in out

Transformer Equation

p

s

p

s

N

N

V

V

Where V = potential difference (voltage)

N = # of turns in coil

Subscript p refers to primary coil

Subscript s refers to secondary coil

Example: A step up transformer is used on a 120 V line to provide a potential difference of 2400 V. If the

primary has 75 turns, how many turns must the secondary have?

p

s

p

s

N

N

V

V

Vp = 120 V

Vs = 2400 V

Np = 75 turns

Ns = ?75120

2400 sN

Ns = 1500 turns

Power for a transformer• The power into a transformer equal the

power out of a transformer

s

p

p

s

I

I

V

V s

p

p

s

p

s

I

I

N

N

V

V