Download Electromagnetic Induction Faraday`s Law

Electromagnetic
Induction
Faraday’s Law – Part II
1831
PHYS 219 Test III
Thursday; December 17, 2009
8AM
PHYS 112
Lecture 14
Faradays’ Law –
Electromagnetic Induction
Magnetic
flux
ΦB = B ⋅ A
ΔΦ B
E =−
Δt
What is Magnetic Flux?
Magnetic Flux is the product of an area (m2)
with a component of a magnetic field (T)
passing perpendicularly through it.
Convenient to
define area
vector A
ΦB = BA cos(Θ)
Units: ΦB = T•m2=1 Weber = 1 Wb
What is the magnetic flux
through the surface?
=3.0 m2
=2.0 T
=60o
ΦB = BA cos(Θ)
=2.0 T × 3.0 m2 × cos(60o)
=6.0 × 0.5 Tm2= 3Wb
Review: You need to know the direction of the
magnetic field produced by current in a wire
Long straight wire
Wire loop
I
B
Faraday’s Law: An induced emf is produced in a coil
whenever the magnetic flux changes with time.
∆ΦB
E =-N
∆t
Subtle Point: The negative sign
indicates that the induced emf
acts to “oppose” the change in
magnetic flux that causes it.
Key Idea: An emf is produced by the changing magnetic flux.
The emf in turn produces an induced current I.
What is the induced emf if the magnetic field through
a six turn coil increases at a rate of 0.17 T/s?
E=-
ΔΦ B
Δ( B i A)
ΔB
=−
= −A
Δt
Δt
Δt
A = π R 2 = 0.88 m 2
E=−
The negative sign
indicates that the
induced emf acts to
“oppose” the change in
magnetic flux that
causes it
ΔB
= +0.17 T/s
Δt
E = -(0.88 m 2 )(0.17 T/s)= - 0.15 V
Since coil has six turns, E = 6 × (- 0.15)= - 0.90 V
Induced Voltage: a simple example
What is Va-Vb?
N=1
Uniform B
B
ro = 1m
constant rate
of reduction
1 T
a
time
b
0.001 s
Lenz’s Law (1804-1865)
An induced current must flow in the loop to produce a magnetic
field (inside the loop) that opposes the change in flux.
Lenz’s Law – Predicting the direction
of the induced current
(Focus on the Change in Flux w.Time)
a)
b)
motion toward
loop
Iind
Iind
N
N
motion away
from loop
loop
ΦΒ
loop
ΦΒ
increasing time
increasing time
The induced current always produces a magnetic
field that opposes (counteracts) the change in flux
It is often easier to take the absolute
value of Farady’s Law to find the
magnitude of the induced emf and use
Lenz’s Law to find the direction of the
induced current that results.
A Transformer: Trapping Flux with
an Iron Core
iron
core
Coil 2
Coil 1
Electric transformers
Input voltage must
vary with time
For an ideal
transformer
ΔV1 N1
=
ΔV2 N 2
I 2 N1
=
I1 N 2
A transformer has 10 turns on the primary and
100 turns on the secondary. If 110V is applied to
the primary, how much voltage appears across the
secondary?