Electromagnetic Induction

AP Physics

Chapter 21

Electromagnetic Induction

21.1 Induced EMF

Induced EMF

Michael Faraday – a changing magnetic field can produce an electric current

This is an induced current

21.1

Induced EMF

A magnet moved quickly into a coil of wire induces a current

When it is quickly moved the other way, a current is induced in the opposite direction

21.1

Electromagnetic Induction

21.2 Faraday’s Law of Induction; Lenz’s Law

Faraday’s Law of Induction; Lenz’s Law

From experiments the induced emf depends on

1. Rate of change of the magnetic field

2. Loop’s area

3. Angle

Magnetic flux is the

total number of

magnetic field line

passing through

the are enclosed by the loop 21.2

Faraday’s Law of Induction; Lenz’s Law

Magnetic Flux

When is 90, no field lines pass through the loop

The unit for magnetic flux

is a weber

21.2

cosBAB

S-136

A wire that forms a loop that is 25 cm on a side and is placed in a 4T magnetic field. A current of 10 A is then run through the wire. What is the maximum and minimum torque that can be applied to the wire under these

circumstances?

Faraday’s Law of Induction; Lenz’s Law

Since the induced EMF is the rate of change of flux

This is Faraday’s Law of Induction

For multiple loops in a magnetic field

Where N is the number of loops in the field 21.2

tB

tN B

S-138

A wire loop with a diameter of 25 cm goes from being perpendicular to a magnetic field to parallel in 0.3s. The field strength is 10T.

A. What is the change in magnetic flux?

B. What is the induced EMF?

C. If the field points into the board, and the left side of the loop is rotation out of the board, what is the direction of the induced current?

Faraday’s Law of Induction; Lenz’s Law

Lenz’s Law – a current produced by an

induced emf moves in a direction so that its

magnetic field

(produced by

the current)

opposes the

original change

in flux

21.2

Faraday’s Law of Induction; Lenz’s Law

Steps in problem solving – Lenz’s Law

1. Determine if the magnetic flux inside the loop is decreasing, increasing, or unchanged

2. The magnetic field due to the induced current

a. Points in the same direction as the external field if the flux is decreasing

b. Points in the opposite direction if the flux is increasing

c. Is zero if the flux is not changing 21.2

Faraday’s Law of Induction; Lenz’s Law

Steps in problem solving – Lenz’s Law

3. Use the right hand rule-1 to find the direction of the induced current

4. Always keep in mind that there are two magnetic fields

a. An external field whose flux must be changed if it is to induce an electric current

b. A magnetic field produced by the induced current

21.2

S-139

A rectangular wire loop that has sides of 1.2 m spins in a magnetic field so that it makes a complete revolution every 2.4s. If the magnetic field that it spins through has a field strength of 1.9T, how many loops are required to produce a maximum potential difference of 120V?

Electromagnetic Induction

21.3 EMF Induced in a Moving Conductor

Faraday’s Law of Induction; Lenz’s Law

If the rod above is made to move at a velocity v

The area of the rod increases

So the change in area is

The induce EMF is21.3

tvx tlvxlA

tB

t

AB

t

tBlv

Blv

Faraday’s Law of Induction; Lenz’s Law

Sometimes called motional emf

True as long as components are mutually perpendicular

21.3

S-139

A dog with a mass of 3.5 kg is floating in space. He has 25.8x1018 extra electrons placed on him.

A. What is the charge on the dog?

B. The magnetic field of the earth at the point he is floating is 7T. What is the force on the dog?

C. What is the net force on the dog if his rocket pack is thrusting him at a constant 85 m/s parallel to the magnetic field?

Electromagnetic Induction

21.4 Changing Magnetic Flux Produces an Electric Field

Changing Magnetic Flux Produces Electric Field

Since there is an induced current when there is an induced EMF, there must be an electric field

A changing magnetic field induces and electric field

So since

And

The electric field must be21.4

qvBF

q

FE

q

qvBE vBE

S-140

An alpha particle (2 protons, 2 neutrons) is shot upward into a 5T magnetic field that is directed into the plane of the board. It is traveling at 200,000 m/s when it enters the field.

A. What is the force on the particle?

B. What is the diameter of the arc that it travels through?

Electromagnetic Induction

21.5 Electric Generators

Electric Generators

Generator – converts mechanical energy (spinning) into AC current.

If we look at just one perpendicular arm of the loop

Since we have two arms in each loop

Now if we add loops

21.5

Generator Simulation

sinBlv

sin2Blv

sin2NBlv

S-141

A 250 kg fat dude is standing on a slope that makes an angle of 52o with the horizontal. If the coefficient of friction is 0.22, what is his acceleration down the slope?

Funny

S-142

A electron is accelerated through 10V and then injected perpendicular to a 25T field pointed downward. What is the centripetal force acting on the electron?

S-143

Happy Test Day