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week3

# week3 - Physics 1C Faradays Law = Week 3 notes W Gekelman#\$...

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1 Physics 1C Week 3 notes© W. Gekelman Faraday’s Law ! = " #\$ B # t leads us to the concept of inductance. If one part of a circuit produces a changing magnetic flux and this in turn goes through a loop in another part of a circuit or in an adjacent circuit it will induce a voltage and perhaps a current there. In this case the solenoid has a changing current which means there is a changing flux in the 3 loop circuit wrapped around it. The magnetic B is always directly proportional to the current (this is true in Amps law or the Law of Biot and Savart) If B is proportional to the current, i, so is the flux ! B and therefore so is the EMF ! = " #\$ B # t = " stuff ( ) di dt . Let us define this stuff to be L, the inductance. Therefore ! = " #\$ B # t = " L di dt . The inductance depends only upon the geometry. Consider two circuits one next to another

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2 A changing current in coil 1 will induce a changing current in coil 2 ! 2 = " N 2 d # 21 dt . N 2 is the number of turns in coil2 and ! 21 is the flux in coil 2 because of the changing currents in coil 1. Since the flux is proportional to the inductance: ! 2 = " M 21 di 1 dt . This is the EMF in 2 because of the changing currents in 1. M 21 is called the mutual inductance in 2 due to 1. This works both ways: ! 1 = " M 12 di 2 dt . This isn’t everything! Consider a solendoil with a changing current in it. If the solenoid has N turns then the first N-1 turns produce a changing flux on the last turn, which causes a counter or back EMF on it. The changing flux when you sum this up will have a total EMF that opposes the changing current and will be in the opposite direction as the original EMF (or Volatge) the drove the current. The inductance of a coil due to itself is called the self inductance, L, and is given by: (1) ! = " N d # B dt = " L di dt L = N # B i i is the instantaneous current in the coil and Φ B is the flux through the coil due to its own current.
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week3 - Physics 1C Faradays Law = Week 3 notes W Gekelman#\$...

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