Physics 202, Lecture 17

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Physics 202, Lecture 17

• Todays Topics
• Inductance (Ch 32)
• Reminder of Faradays and Lenzs Laws
• Self Inductance
• Mutual Inductance
• Energy Stored in B Field
• RL Circuits

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Review Faradays Law of Induction

• Faradays Law in plain words When the magnetic
  flux through an area is changed, an emf is
  produced
• along the closed path enclosing the area.
• Quantitatively

conventional direction of e
B
q
A
Note the - sign
3
Review Lenzs Law

• Lenzs law in plain words the induced emf always
  tends to work against the original cause of flux
  change

4
Self Inductance

• When the current in a conducting device changes,
  an induced emf is produced in the opposite
  direction of the source current ? self inductance

• The magnetic flux due to self inductance is
  proportional to I
• The induced emf is proportional to dI/dt

L Inductance, unit Henry (H)
5
Exercise Calculate Inductance of a Solenoid
Area A

• show that for an ideal solenoid
• (see board)

of turns N
Reminder magnetic field inside the solenoid (Ch
30)
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Mutual Inductance

• For coupled coils
• e2 - M12 dI1/dt
• e1 - M21 dI2/dt
• Can prove (not here)
• M12M21M
• ? M mutual inductance
• (unit also Henry)
• e2 - M dI1/dt
• e1 - M dI2/dt

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Examples of Coupled Coils (Transformers)
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Energy Stored in a Magnetic Field

• When an inductor of inductance L is carrying a
  current changing at a rate dI/dt, the power
  supplied is
• The work needed to increase the current in an
  inductor from zero to some value I

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Energy in an Inductor

• Energy stored in an inductor is U ½ LI2
• This energy is stored in the form of magnetic
  field energy density uB ½ B2/m0 (recall
  uE ½ e0E2)
• Compare
• Inductor energy stored U ½ LI2
• Capacitor energy stored U ½ C(DV)2
• Resistor no energy stored, (all energy
  converted to heat)

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Basic Circuit Components
e
r
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RL Circuit

• An inductor and are resistance constitute a RL
  circuit
• Any inductor has a resistance, R
• R could also include any other additional
  resistance
• When the current starts to flow a voltage drop
  will occur a the resistance and the inductance
• Once current stabilizes, reaches maximum of

12
Exercise Turn on RL Circuit
Apply Kirchhoff loop rule
13
Exercise Turn on RL Circuit (cont)
Note the time constant is tL/R Quiz What is
the current when t ?
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Exercise Turn off RL Circuit
Apply Kirchhoff loop rule
15
Exercise Turn off RL Circuit (cont)
Note the time constant is tL/R Quiz What is
the current when t ?