Electromagnetic Induction

What’s Next?

Electromagnetic Induction Faraday’s Discovery Electromotive Force Magnetic Flux Electric Generators Lenz’s Law Self-Inductance Transformers

What do we know? Hans Christian Oersted showed that moving

charges create a magnetic field.

Faraday’s Hypothesis

If moving charges produced a magnetic field, could a moving or changing magnetic field produce a current?

Faraday’s Discovery

Faraday discovered that he could induce current by moving a wire loop through a magnetic field or moving the magnetic field through a wire loop.

Faraday’s Discovery is known as Electromagnetic Induction

Faraday's Discovery

Electromotive Force Last week we learned the Lorentz Force.

FB = qvB sinθ = BIL sinθ

When a conductor moves through a magnetic field, a force is exerted on these charges causing them to separate, inducing an EMF.

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vF

+

-

L

Electromotive Force We know: W = Fd and V = W/q.

V = Fd/q

Using algebra and solving for F:

F = Vq/d F = qvB

Set these two relationships equal to one another and then solve for V, which will now be represented as EMF:

EMF (V) = vBL

Where: L is the length of a conductor passing through a magnetic field.EMF = Electromotive Force (Volts)

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I

vF

I

-

+

Electromotive Force The EMF results when the conductor has a velocity

component perpendicular to the magnetic field.

Use RHR #1 where the thumb points in the direction of the velocity. The force on the bar is opposite the velocity.

I

Example 1: EM Induction

A segment of a wire loop is moving downward through the poles of a magnet, as shown. What is the direction of the induced current?

a. The current direction is out-of the page to the left.b. There is no induced current.c. The current direction is into the page to the right.

Example 2: EM Induction The drawing shows three identical rods (A, B, and C)

moving in different planes in a constant magnetic field directed along the +y axis. The length of each rod and the speeds are the same, vA = vB = vC. Which end (1 or 2) of each rod is positive?

Rod A:

a. 1 b. 2 c. neither

Rod B:

a. 1 b. 2 c. neither

Rod C:

a. 1 b. 2 c. neither

Electromagnetic Induction

Why is it important? Motors Generators Transformers

Electric Generators Invented by Michael Faraday. Convert mechanical energy into electrical

energy. Similar to an electric motor, but function in an

opposite manner. Electrical power generation is the foundation by

which electricity is supplied to homes and businesses around the world.

Electricity is generated in many ways - hydroelectric, nuclear, coal, gas, oil fired, wind solar, geothermal.

Magnetic Flux

What is magnetic flux? Like electric flux A measure of the strength of the magnetic field, B,

passing through a surface perpendicular to the field. For a bar magnet, the flux is maximum at the poles. The more magnetic field lines, the higher the flux.

=BAcos

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Iv

F

I

-

+

Magnetic Flux and EMF We already know:

EMF = vBL

v = Δx/Δt = (x – xo)

(t – to)

EMF = (Δx/Δt)BL = (xL – xoL) B = (BA) – (BAo)

(t – to) (t – to)

EMF = -ΔΦ/Δt Where:

= BA cos and = the angle the normalto the surface makeswith B (in this drawing itis 0o).

Faraday’s Law of EM Induction In the drawing on the previous slide, there is only

one loop in the circuit. When there is more than one loop in a circuit, as

in the coil of a solenoid, the EMF induced by a changing magnetic field will increase by a factor equal to the number of loops in the coil.

EMF = -N ΔΦ/Δt

Where N = the number of loops in the coil.

Note: The units for Φ are Webers (Wb) or 1 Tm2

Magnetic Flux & Generators

• x

v

v

x

• v

B

v

v

•

xI

Zero CurrentMin Change in Flux

Max CurrentMax Change in Flux

w

Direction of Rotation

Axis of Rotation

v

Magnetic Flux & Generators When the armature is at 90o with the magnetic

field, the current will be zero because the rate of change in magnetic flux through the coil will be at a minimum.

When the windings of the armature are aligned with the direction of the magnetic field, the current will be at a maximum because the rate of change in magnetic flux will be at a maximum.

Principle Operation and Characteristics of a Generator The armature turns such that the coils of wire

cut through the magnetic field inducing an EMF in the coil.

The magnetic field or the conductor need to be moving in order for an EMF to be generated.

The greater the change in magnetic field, the greater the EMF, ie. the faster the armature turns, the greater the power produced.

Use RHR #1 to determine the direction of current through the coil.

Generator

Lenz’s Law The induced EMF resulting from a changing

magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

If the magnetic field is increasing, a current will develop to oppose the increasing magnetic field.

If the magnetic field is decreasing, a current will develop to create a magnetic field in the same direction as the one that is decreasing.

A current will form that attempts to keep the magnetic field constant.

Lenz’s Law abides by the laws of conservation of energy.

Lenz’s Law

Lenz's Law

Lenz’s Law

Current will be induced in the copper ring when it passes through a region where the magnetic field changes. When the magnetic field is constant or absent, their will be no induced current.

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No Current

No Current

No Current

InducedCurrent

InducedCurrent

Applications of Lenz’s Law (Eddy Currents) Eddy current balances. Eddy current dynamometer. Metal detectors (Lenz's Law) Braking systems on trains. What are Eddy currents?

Eddy currents are currents created in conductors to oppose the changing magnetic fields they are exposed to.

Eddy currents respond to the changes in an external magnetic field.

Eddy currents can form in conductors even if they are not capable of being magnetized.

Lenz’s Law and Motors – Back EMF When a current carrying wire moves in a

magnetic field, an EMF is produced called the back EMF.

The back EMF opposes the current in the motor resulting in a decrease in the total current through the motor.

As the motor slows down, the current will increase.

Back EMF’s may cause sparks at outlets and switches when circuits are disconnected while in use.

Back EMF in Electric Motors

Both motors and generators consist of coils that rotate in a magnetic field. There are two sources of EMF:

• An applied EMF to drive the motor.• An EMF induced (back EMF) by the generator like

action of the coil that opposes the applied EMF.

EMFnet = Vapplied – EMFinduced

I = (Vapplied – EMFinduced)/R

Transformers Transformers are used to

increase or decrease AC voltage. Transformers that increase

voltage are called step-up transformers.

Transformers that decrease voltage are called step-down transformers.

Transformers efficiently change voltages with little loss of energy.

Transformer Design Transformers consist of

two windings wrapped around an iron core.

The iron core is easily magnetized and will enhance the magnetic field.

Mutual Inductance: The changing current in one coil (primary) will induce an EMF in the other coil (secondary).

Transformers (cont.) The EMF induced (secondary voltage, Vs) in a secondary

coil is proportional to the primary voltage (Vp). The EMF induced is also proportional to the number of

windings (Ns) in the secondary coil. The EMF is inversely proportional to the number of

windings in the primary coil (Np).

Vs/Vp = Ns/Np

Pp = Ps

VpIp = VsIs

Rearranging: Is/Ip = Vp/Vs = Np/Ns

Power losses are minimal for transformers

Key Ideas Electromagnetic induction: is the process by

which current is generated by moving a conductor through a magnetic field or a magnetic field through a conductor.

The induced current is maximum when the relative motion of the conductor is perpendicular to the magnetic field.

The induced voltage is called EMF (=vBL). Magnetic flux is a measure of the strength of the

magnetic field passing through a surface. A generator is a device that converts mechanical

energy into electrical energy. Generators are similar to motors.

Key Ideas Lenz’s Law: The induced EMF resulting from a

changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

Self-Inductance: A changing current in a coil will induce an EMF that opposes the change in current.

Transformers convert high voltage/low current electrical energy to low voltage/high current electrical energy.

Transformers consist of two coils (primary and secondary) wrapped around a common iron core.