AC CircuitsEddy currents (sec. 29.6)
Displacement Current (sec. 29.7)
Electromagnetic Induction Ch. 29
OVERVIEW
Learning Goals - we will learn: ch 29
• The experimental evidence that a changing magnetic field induces an emf !
• How Faraday’s Law relates the induced emf in a loop to the change in magnetic flux through the loop.
• How a changing magnetic flux generates an electric field that is very different from that produced by an arrangement of charges.
• Four fundamental equations completely describe both electricity and magnetism.
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When B is constant and the shape, location, and orientation of the coil does not change, the induced current is zero
in the coil.
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Lenz’s law
Lenz’s Law
The induced emf (or current) always tends to oppose or cancel the change that caused it.
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How electric generators, credit card readers, and transformers work.
A changing magnetic flux causes (induces) an emf in a conducting loop.
C 2004 Pearson Education / Addison Wesley
Eqn 29.3
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Lenz’s law
Lenz’s Law
The induced emf (or current) always tends to oppose or cancel the change that caused it.
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e = DV = energy / charge = W/q
e = DV = work / charge
DV = (q v B) L / q
so
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A capacitor being charged by a current iC has a “displacement current” between the plates equal to iC , with displacement current iD = e A dE/dt. This changing E field can be regarded as the source of the magnetic field between the plates. ( E _ B )
DISPLACEMENT
CURRENT
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A capacitor being charged by a current iC has a displacement current equal to iC between the plates, with
displacement current iD = e A dE/dt
From C = e A / d and DV = E d we can use
q = C V to get
q = (e A / d ) (E d ) = e E A = e F E and
from iC = dq / dt = e A dE / dt = e dF E / dt = iD
We now see that a
changing E field can produce a B field,
and from Faraday’s Law, a
changing B field can produce an E field or emf.
C 2011 J. Becker
C 2004 Pearson Educational / Addison Wesley
The relationships between electric and magnetic fields and their sources can be stated compactly in four equations, called
Maxwell’s equations.
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Lenz’s law
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Direction of induced current through R = ? when switch is closed, opened, coils are moved closer, R is decreased?
Lenz’s law (Exercise 29.18)
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Direction of induced current through R when current goes into, out of terminal a, input current is increasing or decreasing?
Motional emf and Lenz’s law
(Exercise 29.21)
(Exercise 29.26)
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Determine induced current directions as loop passes into, through, and out of B field.
TRANSFORMERS
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Direction of induced current through R when current goes into, out of terminal a, input current is increasing or decreasing?
Transformer: AC source is V1 and secondary provides a voltage V2 to a device with resistance R.
TRANSFORMERS
e2 /e1 = N2/N1
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Figure 32.2b
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OVERVIEW