Mutual Induction



"A fact is a simple statement that everyone believes.  It is innocent, unless found guilty.  A hypothesis is a novel suggestion that no one wants to believe.  It is guilty, until found effective"
Edward Teller
magmutualindfig1
magmutualindeqn1
but the total flux through circuit 2 is proportional to the current in circuit 1, where the proportionality constant is called the mutual inductance of the coils, M21,

magmutualindeqn2
Combining these two equations gives

magmutualindeqn3
In other words the emf in circuit 2 is proportional to the rate of change of current in circuit 1.  As we will see shortly, the mutual inductance M21 depends only on the geometric configuration of the two circuits.
  • If the roles of the two circuits are reversed - that is a changing current in circuit 2 induces a current in circuit 1 - then
magmutualindeqn4
  • It is "easy" to show that  M21 = M12 .  In other words given two circuits in a particular configuration it doesn't matter in which circuit the current is induced the mutual inductance is the same.
  • UNITS: Inductance is measured in Henrys Henry
magmutualindeqn5
exclamation The concept of inductance is related to the magnetic field in a similar way that capacitance is related to the electric field.
  • In order to calculate mutual inductance you will typically follow the steps below:
  1. Determine B due to one circuit at the location of the other using Ampere's Law or the Biot-Savart Law.
  2. Using this B calculate the magnetic flux through the 'other' circuit.
  3. Then use the equation N2Φ2 = MI1 to obtain M.
You will always find that M depends only on the geometric parameters of the two circuits and the number of turns in each circuit.

This girl said she recognized me from the vegetarian club, but I'd never met herbivore.

 
 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu