HL Electromagnetic Induction

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Agenda:

 _{Good Things!}

 _{Quiz: Diffraction & Polarization}

 _{Notes: Electromagnetic Induction}

 _{Homework: Read Hamper Chapter}

6.7-6.9

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General Summary

 _{Last year we saw how an electric}

current generated a magnetic field

 _{This lesson we see how a changing}

magnetic field (flux) can produce an electric current

 _{We’ll use Faraday’s Law to find the}

value of the induced emf

 _{And Lenz’s Law to find the direction}

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Objectives

 _{Calculate flux or flux linkage}

using

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Objectives

 _{Identify situations in which an}

emf is induced and determine the magnitude of the emf by using Faraday’s law,

Included are cases of a changing

area, a changing magnetic field

or a changing angle between

(5)

Objectives

 _{Find the direction of the induced}

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Review: Magnetic Force on a Moving Charge

 _{A positive charge,}_q_{, moves}

with speed v in a magnetic field, B

 _{In time}_∆t_{, the charge moves a}

distance,

 _{A moving charge is a current,}

and the current has magnitude,

t

v

L





t

q

I

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Magnetic Force on a Moving Charge

 _{The magnetic force on a}

current was previously given as,

 _{where is the angle between}_𝛉

the velocity of the charge and the magnetic field. Therefore,



sin

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 _{The direction of this force is given} to us by our friend, Mr. Hand

 _{This tells us that if the charge}

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 _{Question: An electron}

approaches a bar magnet as

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 _{Question: An electron approaches a bar}

magnet as shown. What is the force on the charge?

 _{The field on a bar magnet runs from N to S so the}

lines run to the left at the position of the charge. Mr Hand says put your thumb in the direction of the

velocity, up, fingers in the direction of the field, left, and your palm is in the direction of the force on a positive charge, out of the page. Since this is an electron, the force is in the opposite direction, into the page.

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Wire Moving In A Magnetic

Field

_ _{If a wire is made to move}

normally to a magnetic field at constant speed, an emf

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Wire Moving In A Magnetic

Field

 _{The wire is a conductor which}

means it has free and

loose-living electrons that can easily fall prey to evil influences

 _{Mr. Hand says that if you put}

your thumb in the direction of

the velocity, down, fingers in the direction of the field, out of the page,

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Wire Moving In A Magnetic

Field

 _{However, since electrons have such a}

negative attitude, they are going to go in the opposite direction of the friendly positive test charge, so the free and

loose-living electrons will flow to the right.

 _{A flow of electrons is a current. Thus we}

have created a current in a wire just by moving it across a magnetic

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Wire Moving In A Magnetic

Field

 _{What happens when the wire}

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Wire Moving In A Magnetic

Field

 _{What happens when the wire}

stops moving?

 _{Once the movement stops, the}

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Wire Moving In A Magnetic

Field

 _{Since the wire is not connected to}

anything, the current has no place to go, so we build up negative charges on the right side and positive charges on the left side which is an electric

field of magnitude,

 _{E – electric field}

 _{V – potential difference}  _{L – length of wire}

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Wire Moving In A Magnetic

Field

 _{All those electric charges}

building up at each end creates a problem because like charges

repel.

 _{Being held against their will, the}

charges create an electric force,

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Wire Moving In A Magnetic

Field

 _{When the electric force,}_eE_,

pushing the electrons back equals the magnetic force

pushing them towards the ends, the flow of charges (current)

stops

eE – electric force

evB – magnetic force

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Wire Moving In A Magnetic

Field

 _{If you substitute for the electric}

field,

 _{Thus, we have created}

a motional emf

v – velocity

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Faraday’s law

 _{Current is created when a}

conducting wire moves in relation to a magnetic field

 _{It doesn’t matter which one}

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Faraday’s law

 _{Consider the situation below}

 _{Does it matter whether the wire or}

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Faraday’s law

 _{Consider the situation below}

 _{Is there a current if nothing}

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Faraday’s law

 _{Factors that influence flow of}

current:

 _{relative speed of the magnet with}

respect to the coil

 _{strength of the magnet}

 _{number of turns in the coil}

 _{area of the loop}

 _{the angle between the magnet}

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Faraday’s law

 _{Factors that influence flow of}

current:

 _{relative speed of the magnet with}

respect to the coil

 _{strength of the magnet}

 _{number of turns in the coil}

 _{area of the loop}

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Magnetic Flux Through A

Loop

B = magnetic field A = area of the loop

𝛉 = angle between the

magnetic field direction and the direction normal to the loop area, i.e. if the magnetic field direction is perpendicular to the area enclosed by the wire loop, = 0, cos 0 = 1𝛉



cos

BA

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Magnetic Flux Through A

Loop

 _{If the loop has N}

turns of wire

around it, the flux is given by,

 _{and it is now}

referred to as a

flux linkage



cos

NBA

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Magnetic Flux Through A

Loop

 _{The unit for}

magnetic flux is the Weber (Wb), 1Wb = 1T∙m2

 _{Max flux occurs}

when = 0°, 𝛉

perpendicular, and min flux

occurs when = 𝛉

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Magnetic Flux Through A

Loop

 _{To increase flux,}

you must:

 _{increase the loop}

area exposed to the magnetic field,

 _{increase the value} of the magnetic

field,

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Magnetic Flux Through A

Loop

 _{Ultimately, the}

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Magnetic Flux Through A

Loop

 _{Faraday’s Law is}

that the induced emf is equal to the (negative)

rate of change of the magnetic flux,

t

N







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Magnetic Flux Through A

Loop

 _{Note: The minus sign is}

inconsequential since we are only looking for the magnitude of the emf. It does become a factor if using calculus,

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Lenz’s Law

 _{Determining the direction of the}

induced emf

 _{The induced current will be in}

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Lenz’s Law

 _{Consider the following: A bar}

magnet is dropped through a loop of conducting wire

 _{with the North end first,}

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Lenz’s Law

 _{As the North pole enters the}

loop, the flux increases because the magnetic field at the loop is getting bigger as the magnet

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Lenz’s Law

 _{Since the flux is increasing, a}

current is induced to produce a magnetic field that opposes the change in flux, in a direction

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Lenz’s Law

 _{The current flow must be such that}

the magnetic field it produces opposes the increasing magnetic field of the magnet

 _{Thus the magnetic field induced by}

the current must be up

 _{Only a counterclockwise current}

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Lenz’s Law

 Once the magnet passes the

midpoint, the field is now decreasing, which means increasing in the negative direction which means the current will reverse itself

 _{Thus the current will change from}

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Lenz’s Law

 _{When the South pole enters}

first, the same thing

happens, but in reverse

direction, because with the South end entering first,

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Lenz’s Law

 _{Since the flux is ‘decreasing’} (magnetic field running upward with downward movement), a current is induced to produce a magnetic field that opposes the change in flux, in a direction

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Lenz’s Law

 _{Therefore, the only current}

that will produce a

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Lenz’s Law

 _{Once the magnet passes}

the midpoint, the field goes from decreasing to

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Lenz’s Law

 _{If the magnet were to}

continuously pass up and down through the wire,

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Loop Through Magnetic

Field

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Loop Through Magnetic

Field

 _{As the loop enters, the}

flux (the amount of B passing through the loop) increases, so an emf is induced

 _{Flux then is}

where x is the length of loop in the magnetic

field

BLx

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Loop Through Magnetic

Field

 _{The rate of change (the}

emf) is

 _{Therefore the current}

will be,

BLv





R

BLv

R

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Loop Through Magnetic

Field

 _{What will the}

direction of the

(48)

Loop Through Magnetic

Field

 _{What will the}

direction of the

current in the wire be?

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Loop Through Magnetic

Field

 _{Because of the}

magnetic field from the induced current, a force is generated

 _{The force acts on}

the part of the loop inside the magnetic field (L)

 _{Force is directed}

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Loop Through Magnetic

Field

 _{If the loop is to}

maintain constant velocity, a force to the right must be

exerted to overcome the induced force

 _{This means the force}

must do work

R

v

L

B

F

2 2

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Loop Through Magnetic

Field

 _{If the force is doing}

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Objectives

 _{Identify situations in which an}

emf is induced and determine the magnitude of the emf by using Faraday’s law,

Included are cases of a changing

area, a changing magnetic field

or a changing angle between