Chapter 31 Electromagnetic Induction

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Chapter 31 Electromagnetic Induction

• PHYS 2326-20

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Concepts to Know

• Magnetic Induction
• Induced Current
• Induced EMF
• Faradays law
• Lenzs Law
• Motional Electromotive Force
• Induced Electric Fields
• Eddy Currents
• Maxwells Equations
• Superconductivity (Chapter 27.5)

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Faradays Law

• Faradays Law of Induction
• An induced EMF is produced by a changing magnetic
  field.

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Faradays Law

• Assuming a uniform field B at an angle ? to the
  vector area A produces
• EMF -d (BA cos ?)/dt
• Magnitude of B can change with time
• Area enclosed by loop can change with time
• Angle ? between B and A can change with time
• Any combination of the above

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Examples

• Ground Fault Interruption detector
• Electric guitar pickup
• Bicycle speedometer sensor
• Electric transformer
• Generator

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Motional EMF

• Given conductor of length l moving at velocity v
  in magnetic field B
• Electrons in conductor experience magnetic force
  Fb downward creating a negative charge at the
  bottom and a positive charge at the top and
  creating a downward electric field E which
  creates an upward force on electrons Fe

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Fe
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l
E
Fb
V
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Motional EMF

• Charges accumulate until a balance is reached
  where the upward force Fe qE balances with the
  downward magnetic force on the electron Fb qvB
  or E vB
• Using the voltage relation ?V El for
  equilibrium becomes ?V El Blv
• ?V is potential but E is not electrostatic
• This En is an induced EMF
• It is maintained as long as the motion continues

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Motional EMF

• The more general case for the induced EMF when v
  B and l are not mutually perpendicular

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Lenzs Law

• The induced current in a loop is in the direction
  that creates a magnetic field that opposes the
  change in magnetic flux through the area enclosed
  by the loop

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Induced EMF and Electric Fields

• An electric field is created in the conductor as
  a result of the changing magnetic flux
• Independence of test charges suggests that a
  changing magnetic field generates an electric
  field in empty space even without a conducting
  loop
• This is a nonconservative force

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Eddy Currents

• According to Lenzs law currents are induced by a
  changing magnetic flux.
• Eddy currents are induced in bulk pieces of metal
  moving through a magnetic field.
• These are in the direction to create a magnetic
  field to oppose the changes in the existing
  magnetic field.

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Maxwells Equations

• See chapter 34.2
• The basis of all electromagnetic phenomenon

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Superconductivity

• R 0 below a critical temperature
• Once started current appears to flow indefinitely
  and has been observed flowing for several years
• How does one start a current flow?
• Remove a magnetic field
• Add a magnetic field such as lower a permanent
  magnet down onto a plate until it balances
  floating over the surface of the superconductive
  plate

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Example 1

• Given a coil of wire with 100 turns and a radius
  of 5cm and a uniform magnetic field perpendicular
  to the coil plane, an increasing field B with
  rate 0.2T/s and a resistance of 50 0hms, find a)
  the emf induced, d) the direction of the magnetic
  field created by the coil, e) the power required
  to keep the original field increasing by 0.2 T/s
  in the z direction

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Example 1

• r0.05m, N100, B (0.2T/s)t, R 50 O
• emf -N dFB /dt, FB is magnetic flux, A pr2
• A p(0.05)2 0.00785 m2
• B is some unknown value at time t0 but it
  changes at 0.2 T/s so assume its 0 at t0
• FBBA (0.2 t) (0.00785) 0.00157t Tm2
• emf -(100)(0.00157) -0.157V

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Example 1

• b) Current? emf IR, Iemf/R
• I -0.157V/50 -0.00314A -3.14mA
• c) Direction of current? by Lenzs law opposes
  change of B which is increasing in the z
  direction. Therefore the current is flowing to
  create an opposing B field so by right hand rule,
  Bc is z and current is CCW.
• d) See above
• e)P I emf I2 R 0.493mW

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Example 2

• 2 parallel long straight wires separated by
  L30cm are connected by on the left end and a
  sliding bar placed across the two wires and slid
  to the right at v2m/s, This is in the presence
  of the uniform field B10T directed into the
  paper. The bar has 10 Ohms resistance, the rest
  none. Find a) emf induced, b) current in the
  bar, c)magnetic force on the bar, d)power
  required to pull the bar, e) power dissipated in
  the bar

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Example 2

• L 0.3m, xvt A Lx, as a f(t) Lvt
• a) emf dFB /dt, FB BA for uniform field
• FB BLvt so emf vBL (2)(10)(.3) 6V
• Flux into the page is increasing because of A.
  The current generated FB must be out of the page
  by Lenzs law so by RHR current is up.
• b) emf IR , E6/10 0.6 A

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Example 2

• c) eqn 29.10 F ILxB force on a moving current
  carrying wire
• F0.6 0.3 10 1.8N opposing motion (left)
• d)power required, eqn 31.7 PF v
• P (1.8)(2) 3.6 W
• e) dissipation P I2R (0.6)2 10 3.6W