Faraday

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Faradays Law of Induction
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Electromagnetic Induction
In a closed electric circuit, a changing
magnetic field will produce an electric current
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Faradays Law of Induction
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Magnetic Flux

• In the easiest case, with a constant magnetic
  field B, and a flat surface of area A, the
  magnetic flux is
• FB B A cos ?
• Units 1 tesla x m2 1 weber

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Magnetic Flux
What is the flux of the magnetic field In each of
these three cases? a) b) c)
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Find the magnetic flux through the loop
Loop radius r 2.50 cm, magnetic field B
0.625 T.
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Faradays Experiments

• Michael Faraday discovered induction in 1831.
• Moving the magnet induces a current I.
• Reversing the direction reverses the current.
• Moving the loop induces a current.
• The induced current is set up by an induced EMF.

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Faradays Experiments
(right)
(left)

• Changing the current in the right-hand coil
  induces
• a current in the left-hand coil.
• The induced current does not depend on the size
  of
• the current in the right-hand coil.
• The induced current depends on ?I/?t.

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Faradays Law
2)
1)

• Moving the magnet changes the flux FB (1).
• Changing the current changes the flux FB (2).
• Faraday changing the flux induces an emf.

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Lenzs Law

• Faradays law gives the magnitude and direction
  of the induced emf, and therefore the direction
  of any induced current.
• Lenzs law is a simple way to get the directions
  straight, with less effort.
• Lenzs Law
• The induced emf is directed so that any induced
  current flow
• will oppose the change in magnetic flux (which
  causes the
• induced emf).
• This is easier to use than to say ...
• Decreasing magnetic flux ? emf creates
  additional magnetic field
• Increasing flux ? emf creates opposed magnetic
  field

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Lenzs Law

• If we move the magnet towards the loop
• the flux of B will increase.
• Lenzs Law ? the current induced in the
• loop will generate a field B? opposed to B.

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Example of Faradays Law
Consider a coil of radius 5 cm with N 250
turns. A magnetic field B, passing through it,
changes at the rate of ?B/?t 0.6 T/s. The
total resistance of the coil is 8 W. What is the
induced current ?
Use Lenzs law to determine the direction of the
induced current. Apply Faradays law to find
the emf and then the current.
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Example of Faradays Law
Lenzs law ?B/?t gt 0 B is increasing, then the
upward flux through the coil is increasing. So
the induced current will have a magnetic field
whose flux (and therefore field) is down.
I
Induced B
Hence the induced current must be clockwise when
looked at from above.
Use Faradays law to get the magnitude of the
induced emf and current.
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B
FB B A cos ?
I
? - ?FB / ? t
Induced B

• The induced EMF is ? - ?FB / ? t
• In terms of B FB N(BA) NB (pr2)
• Therefore ? - N (pr2) ?B / ? t
• ? - (250) (p 0.0052)(0.6T/s) -1.18 V
  (1V1Tm2 /s)
• Current I ?/ R (-1.18V) / (8 W) - 0.147 A

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Motional EMF
Up until now we have considered fixed loops. The
flux through them changed because the magnetic
field changed with time. Now, try moving the
loop in a uniform and constant magnetic field.
This changes the flux, too.
B points into screen
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Motional EMF - Use Faradays Law
The flux is FB B A BDx This changes in
time ?FB / ? t BD(? x/ ?t) -B D v Hence,
by Faradays law, there is an induced emf and
current. What is the direction of the
current? Lenzs law there is less inward flux
through the loop. Hence the induced current gives
inward flux. ? So the induced current is
clockwise.
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Motional EMF Faradays Law
Faradays Law ?FB/ ?t - ? gives the EMF ? ?
BDv In a circuit with a resistor, this gives ?
BDv IR ? I BDv/R
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A New Source of EMF

• If we have a conducting loop in a magnetic field,
  we can create an EMF (like a battery) by changing
  the value of FB B A cos ?
• This can be done by changing the area, by
  changing the magnetic field, or the angle between
  them.
• We can use this source of EMF in electrical
  circuits in the same way we used batteries.
• Remember we have to do work to move the loop or
  to change B, to generate the EMF (Nothing is for
  free!).

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Motional EMF
What happens when the conducting horizontal bar
falls?
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Motional EMF
What happens when the conducting horizontal bar
falls?

• As the bar falls, the flux of B changes,
• so a current is induced, and the bulb
• lights.

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Motional EMF
What happens when the conducting horizontal bar
falls?

• As the bar falls, the flux of B changes,
• so a current is induced, and the bulb
• lights.
• The current on the horizontal bar is
• in a magnetic field, so it experiences
• a force, opposite to gravity.

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Motional EMF
What happens when the conducting horizontal bar
falls?

• As the bar falls, the flux of B changes,
• so a current is induced, and the bulb
• lights.
• The current on the horizontal bar is
• in a magnetic field, so it experiences
• a force, opposite to gravity.
• The bar slows down, until eventually
• it reaches constant speed (FB mg)

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Eddy Currents
A circulating current is induced in a sheet of
metal when it leaves a region with a magnetic
field. The effect of the magnetic field on the
induced current is such that it creates a
retarding force on the moving object.
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What is the external force necessary to move the
bar with constant speed?
The induced current is I ? / R I B v L /
R The magnetic force on the current is F B I
L F B (BvL/R) L F B2 v L2 /R
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The mechanical power used to move the bar is PM
F v B2 v2 L2 / R The electrical
power dissipated in the circuit is PE I2 R
(B v L / R)2 R PE B2 v2 L2 / R
Mechanical Power to Electrical Power
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Given Bulb R 12 ?, P 5 W Rod L 1.25 m, v
3.1 m/s

• Find
• Magnetic field strength
• External force

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Electric Generator
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Simple Electric Motor