Electromagnetic induction
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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.

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Electromagnetic Induction

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Electromagnetic induction

Electromagnetic Induction


What s next

What’s Next?

  • Electromagnetic Induction

  • Faraday’s Discovery

  • Electromotive Force

  • Magnetic Flux

  • Electric Generators

  • Lenz’s Law

  • Self-Inductance

  • Transformers


What do we know

What do we know?

  • Hans Christian Oersted showed that moving charges create a magnetic field.


Faraday s hypothesis

Faraday’s Hypothesis

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


Faraday s discovery

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

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

+

-

L

v

F

Electromotive Force

  • Last week we learned the Lorentz Force.

    FB = qvB sinθ = ILB

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


Electromotive force1

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)


Electromotive force2

I

+

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

I

F

v

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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

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

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:

    • 1b. 2c. neither

  • Rod B:

    • 1b. 2c. neither

  • Rod C:

    • 1b. 2c. neither


Electromagnetic induction1

Electromagnetic Induction

  • Why is it important?

    • Motors

    • Generators

    • Transformers


Electric generators

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

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


Magnetic flux and emf

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:

    Φ = BA cos and

    • = the angle the normal

      to the surface makes

      with B (in this drawing it

      is 0o).

I

+

x x x x x x

x x x x x x

x x x x x x

x x x x x x

F

I

v

-


Faraday s law of em induction

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 Tm2


Magnetic flux generators

I

x

x

x

Magnetic Flux & Generators

Direction of Rotation

v

v

v

w

B

v

v

v

Zero Current

Min Change in Flux

Max Current

Max Change in Flux

Axis of Rotation


Magnetic flux generators1

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

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

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 law1

Lenz’s Law

Lenz's Law


Lenz s law2

No Current

Induced

Current

x x x x x x

x x x x x x

x x x x x x

x x x x x x

No Current

Induced

Current

No Current

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.


Applications of lenz s law eddy currents

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

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

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


Self inductance

Self-Inductance

  • An increasing current in a coil will induce an EMF that is opposing to the current in the coil.

    NΦ = LI

    Where L is a constant called self-inductance.

    Substituting into Faraday’s Law of induction:

    EMF = -L ΔI/Δt

    Note: the negative sign shows that the EMF is always opposing the change in current.

    Note: the faster the change in current, the greater the EMF.


Transformers

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

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

Power losses are minimal for transformers

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


Key ideas

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 ideas1

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.


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