I. Faraday's Law: An emf can be induced in a circuit if the magnetic flux that passes through the area enclosed by that circuit changes with time.

  induced emf = - (change in flux)/(change in time)

  A. The minus sign indicates the direction of the induced emf.

  B. Since flux depends on the B-field and area, either (or both) could change with time and produce an emf.

II. Lenz's Law: If the circuit is a closed circuit, then the induced current will appear in such a direction that the flux produced by it will be in opposition to the changing flux.

III. Application: A rectangular wire loop passing through a region where the B-field is confined to part of that region.

IV. Time-varying fields

  A. A changing magnetic field produces an electric field. However, this is not due to static charges and we shall call it a non-electrostatic field, En. We shall see in the following example that the integral of En around a closed path is equal to the negative of the change in magnetic field flux through the area enclosed by the path. Recall that for the electrostatic E-field E this same integral would be zero. Why?

V. Inductance

  A. Mutual Inductance

   1. If two wire coils are near each other, a current i in one coil will produce a B-field the other "sees". The flux through the    area enclosed by the second coil will produce an induced emf in the second coil if i changes with time. The concept of    inductance is used to relate the induced emf in the second coil to the change in current in the first coil rather than the    change in flux produced by the first coil.

    mutual inductance = M21 = (flux through coil 2 due to 1)/(current in coil 1)

   2. If the current in coil 1 changes, then the flux through coil 2 will change producing an induced emf in coil 2.

    induced emf in 2 = -M21(di/dt)

  B. Self-inductance

   1. Actually, an induced emf will also appear in a coil if the current in that coil changes with time. This is called    self-induction and a self-induced emf.

    emf = -L(di/dt)              

    where L is the self inductance and depends on the geometry of the coil. Units for inductance: 1 volt-sec/amp = 1 Henry

   C. Inductive devices in circuits

    1. How does an inductive device affect the current in a circuit containing a battery, a switch, a resistor, and a source of emf?