Magnetic Induction. Your new puzzle Pieces Induction What is it? Recall how a current in a wire can cause a magnetic field, well it’s only fair then.

Magnetic Induction

Your new puzzle Pieces

dt

dN B

)sin( tNAB

Induction

• What is it?

• Recall how a current in a wire can cause a magnetic field, well it’s only fair then that a magnetic field can cause (induce) a current in a wire.

• Two Laws to quantify the effect: – Faraday’s – Lenz’s

Applications

• Electric Power generation

• Electric Guitar

• Radio and TV broadcast/reception

• You’ll think of many others for sure by the end of the day!

Let’s get right to it!

• If F = ma is the “mother of all” mechanics Eqn’s

• Then F = qv x B could be the mother of all magnetism eqn’s

qv x B helps explain many electromagnetic effects

• Motion of charged particle in a magnetic field.• Force on a current carrying wire in a magnetic

field.• If you move a conductor in a magnetic field, the

“free” electrons experience a Force of F=qv x B, they tend to move, that’s a current!

• Voltage induced in a conductor moving through a magnetic field

• Current induced in a conducting loop

Faraday’s Law

• The electromotive force, emf, (think voltage) induced in a circuit equals the time rate of change of the magnetic flux through the circuit.

dt

dN B

Lenz’s Law

• The polarity of the emf opposes the change in magnetic flux, it tends to maintain the flux present before the change, think inertia .

Magnetic Flux B

• So what’s with Flux?– Magnetic field times area, how much

magnetism passes through an area,– Think through a conducting loop

B = BAcos

B is field Strength, A is area is angle between field and normal to the plane of the coil.

B

B

A

B = BAcosComponent of B that goes through the loop.

Problem#1

• A square loop of copper with area =0.5m2 is perpendicular to a magnetic field of 1.2T. It is pulled out of the field in 2.4 sec. What is average emf induced in the loop?

t=2.4sec

B=1.2T

A=0.5m2

Problem #2a

R= 100

d=20cm

B= 1.25T

vbar=3000m/s

What is the emf induced in the bar?

Problem #2b

R

B

vbar

What is direction of the induced current in the “loop”(clockwise or counter clockwise)?

Point right thumb in direction OPPOSING increasing flux.Flux increases into page here, so thumb point out of page.Fingers wrap counterclockwise, so that is the direction of induced current.

• Pulling out a hoop is cool at the circus, but it’s a bit more practical to spin the loop…if you want to make electricity.

Calculus is great!

• Faraday said the induced emf is the time rate of change in magnetic flux

BAcosdN

dt

If B and A are constants…and t

sin( )NAB t

BdNdt

B = BAcos

Problem # 3

• Let’s spin the 0.5 m2 loop at 100 rad/s in a 1.2 T magnetic field and find the induced voltage.

B=1.2T

A=0.5m2

Induced current

• Generators

sin( )

V IR

NABI tR R

Alternating current

Problem # 4

• Now my 0.5m2 loop has 100 turns, resistance of the device attached is 10 ohms, and the induced current is 0.10 Amps. What must be the rate of change of the magnetic field?

B, dB/dt

Self-Inductance

• OK so an electrical current can cause a magnetic field.

• A changing magnetic field can cause an induced current…

• Can an electrical circuit induce a magnetic field that induces a current in the circuit that caused the magnetic field?

• YES!

Self-Inductance

• Once a current is established in a circuit, self inductance will tend to keep the current going even after the circuit is turned off…

• No it isn't perpetual motion.

• The current will decay to zero in a short time, but not instantly.

Solenoid

• A solenoid is a coil of wire such as is used to change voltage. Think transformer.

• It has an inductance given by: l

ANL

20

Lenz’s Law

• So the emf opposes the change in magnetic flux, that amounts to the induced voltage and current being directed opposite the applied voltage

BdNdt

Check this out…What if we disconnect the voltage, that’s decreasing the flux, so the solenoid will tend to keep the current going in the same direction it was before!!!

Problem # 5

Let’s design a generator. I want to generate 120 volts. My loop can only be 0.10 meters in diameter. I can only turn it at 3000 rpms. We can only wrap 400 turns around the rotor. How strong must the magnetic field be?

B

Your new puzzle Pieces

dt

dN B

)sin( tNAB

Problem # 5

Let’s design a generator. I want to generate 120 volts. My loop can only be 0.10 meters in diameter. I can only turn it at 3000 rpms. We can only wrap 400 turns around the rotor. How strong must the magnetic field be?

B