Walker, Chapter 23 Magnetic Flux and Faraday

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Walker, Chapter 23Magnetic Flux and Faradays
Law of Induction
Michael Faraday, portrait by Thomas Phillips
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Induced EMF (Voltage) from changing Magnetic Flux

• Electric currents produce magnetic fields.
• 19th century puzzle, can magnetic fields produce
  currents?
• A static magnet will produce no current in a
  stationary coil
• Faraday If the magnetic field changes, or if
  the magnet and coil are in relative motion, there
  will be an induced EMF (and therefore current) in
  the coil.
• Key Concept The magnetic flux through the coil
  must change, this will induce an EMF e in the
  coil, which produces a current I e/ R in the
  coil.
• Such a current is said to be induced by the
  varying B-field.

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Magnetic Flux

• For a loop of wire (not necessarily circular)
  with area A, in an external magnetic field B, the
  magnetic flux is

q
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Walker problem 2 A uniform magnetic field of
0.0250 T points vertically upward. Find the
magnitude of the magnetic flux through each of
the five sides of the open-topped rectangular box
shown in the figure, given that the dimensions of
the box are L 31.5 cm, W 12.0 cm, and H
10.0 cm.
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Question Magnetic Field from loop

• Current I flows around the loop as shown, driven
  by the battery. Inside the loop the magnetic
  field generated by current I is
• Out of screen
• Into screen

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Magnetic flux generated by current in loop.

• ? ?
• ? ?
• ? ?

• In this case, we choose clockwise to be positive
  current.
• In the plane of this picture, the magnetic field
  generated by this current is into the picture
  inside the loop, and out of the picture outside
  of the loop.

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Examples of Induced Current
Any change of current in primary induces a
current in secondary. The secondary shows a
deflection only during the instant just after the
switch is closed or opened.
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Induction by Relative Motion
v

• When a permanent magnet moves relative to a coil,
  the magnetic flux through the coil changes,
  inducing an EMF in the coil.
• In a) the flux is increasing
• In c) the flux is decreasing in magnitude.
• In a) and c) the induced current has opposite
  sign.

v
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Faradays Law of InductionLenzs Law

• Faradays Law The instantaneous EMF in a circuit
  (w/ N loops) equals the rate of change of
  magnetic flux through the circuit

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Question Changing Magnetic Flux

• This is a plot of magnetic flux (WbTm2) through
  a coil.
• For which interval (a, b, or c) is the change in
  flux 0?

c
a
b
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Walker, Problem 23-9

• A 0.25 T magnetic field is perpendicular to a
  circular loop of wire with 50 turns and a radius
  15 cm.
• The magnetic field is reduced to zero in 0.12 s.
• What is the magnitude of the induced EMF? (answer
  7.35 V)

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Inductance

• Consider a solenoid of length l with N windings
  and radius r (Area Ap r2).
• A current I produces a magnetic field in the
  solenoid of
• B m0 N I / l
• This produces a total flux through each winding
  of
• F A B (m0 N A / l ) I
• Define the Inductance L (m0 N2 A / l ) (not a
  length!!)
• If the current in the solenoid changes, there
  will be an induced EMF
• e - N DF/Dt - (m0 N2 A / l ) (DI/Dt)
• e - L (DI/Dt)

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Inductance
Walker Problem 42 Determine the inductance of a
solenoid with 650 turns in a length of 25 cm. The
circular cross section of the solenoid has a
radius of 4.0 cm. answer 10.7 mH
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Example of Inductance

• Consider Solenoid from previous example,
• Radius r 5cm, length l 10 cm, 3500 windings.
• L (m0 N2 Area / l ) (m0 N2 p r2 / l )

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Transformers

• Microscopic currents in soft iron yoke amplify
  magnetic field produced by coils, and contain all
  magnetic field lines to magnetic circuit formed
  by iron.
• Both primary and secondary circuits experience
  the same magnetic flux for each winding, but have
  different number of windings.

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Flux in Transformer
F flux through a single winding or either coil.
(produced by currents in either or both
circuits) EMF(primary) - NP DF/Dt EMF(secondary
) - NS DF/Dt eP / eS NP / NS Energy
conservation requires eP IP eS IS IP / IS
NS / NP
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Walker problem 61 A step-up transformer has 20
turns on the primary coil and 500 turns on the
secondary coil. If this transformer is to produce
an output of 4600 V with a 12 mA current, what
input current and voltage are needed? answer
0.3 A, 184 V