p212c31: 1 Chapter31: Inductance Currents create magnetic fields Changing currents create changing magnetic fields Changing magnetic fields induce EMF’s Circuit elements interact magnetically!

p212c31: 2 Mutual Inductance Magnetic Interaction between two circuits i1i1 B2B2

p212c31: 3 Mutual Inductance: Units [M] = [  ]/[I]=(T m 2 )/(A) = Henry (H) Depends upon Geometry (Magnetic) material properties

p212c31: 4 Example: Long Solenoid with Length l, area A and N 1 turns surrounded by a coil with N 2 turns. A

p212c31: 5 Self Inductance Circuit elements of same circuit link magnetically B I

p212c31: 6 Example: Solenoid from previous example

p212c31: 7 Inductors Schematic symbol Induced EMF (Lenz’s Law) Switch closes, current increases Inductor opposes increase  opposes battery. Steady current (i constant)  no EMF. i  

p212c31: 8 Magnetic Field Energy Energy stored in an inductor I

p212c31: 9 Energy stored in a magnetic field Uniform Magnetic field  energy is distributed uniformly

p212c31: 10 Example: How big an inductor would be required to store 150kWh of energy using a coil carrying 200 A? Example: What is the energy density associated with the design field strength produced by the magnets for the ill fated SSC?

p212c31: 11   a b   a b i i increasing   a b i decreasing Potential differences across inductors in circuits V ab depends upon rate of change of current

p212c31: 12 Homework: How do inductors combine in circuits? -in series? Hints: currents are the same, EMF’s add -in parallel? Hints: EMF’s are the same, currents add Look at derivation for resistors!

p212c31: 13 The R-L Circuit i     E L R

p212c31: 14 i E /R t = 

p212c31: 15 i     E L R

p212c31: 16 i IoIo t = 

p212c31: 17 The L-C Circuit i   L   qq  q

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p212c31: 19 Q t q QQ i t

p212c31: 20 The L-R-C Circuit i   L   qq  q C R  

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p212c31: 23 The Driven L-R-C Circuit i   L   qq  q C R   v(t)= Vcos(  t)

p212c31: 24

p212c31: 25 Q/Q resonance  o