Download Faraday`s Law

Faraday’s Law
Area Change
 The sliding bar creates an emf
by changing the area in the
magnetic field.
• Constant magnetic field
 The potential was due to the
time rate of change of area.
BA
V  vBL 
t
Field Change
 An emf can also be generated
by changing the magnetic field.
 The time rate of change of the
field through a fixed loop
provides the potential.
A B
V 
t
Field Orientation
 The emf depends on the
change in field or the change
in area.
• Area perpendicular to the field
 This suggests that the product
of the field and area
perpendicular matters.
 A B   AB cos  
V 

t
t
Magnetic Flux
 The product of the field and area perpendicular to the
field is the magnetic flux.
M  AB cos
 The magnetic flux is measured in webers.
• 1 Wb = 1 T m2
 The magnetic field can be thought of as a flux density.
M
B
A
Faraday’s Law
 The flux can be used to get
the induced emf.
• Sign indicates polarity
 M
 
t
 This is Faraday’s Law of
induction.
 For multiple turns the emf is
multiplied.
• N turns of wire
• N is the flux linkage
 M
  N
t
Coil Flux
 A circular flat coil has 200
turns of wire with a total
resistance of 25 W and an
enclosed area of 100 cm2.
 There is a perpendicular
magnetic field of 0.50 T that is
turned off in 200 ms.
 Find the current induced in the
coil.
 This problem has three parts.
 To get the current from the
resistance the voltage is
needed.
 To get the voltage the flux is
needed.
• Flux linkage works, too
 Find the flux first.
Flux to Current
 The magnetic flux is  = BA.
•  = (0.50 T)(100 cm2)
•  = (0.50 T)(0.010 m2)
•  = 0.0050 T m2
 The induced current comes
from Ohm’s Law.
• I = V/R
• I = (5.0 V) / (25 W)
• I = 0.20 A
 The change in flux is
negative since it is turned off.
 The induced emf is
E = N /t
E = -(200)(-0.0050 Tm2) /
(0.20 s)
• E = V = 5.0 V
•
•
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