Lectures 17&18: Inductance Learning Objectives To understand and to be able to calculate Self-Inductance To be able to obtain an expression for the Energy Stored by an Inductor To understand and to be able to calculate Mutual-Inductance Self Inductance When current in the circuit changes, the magnetic flux changes also, and a self-induced voltage appears in the circuit. This is a direct consequence of electromagnetic induction dealt with in the previous two lectures.

(a) Definition used to find L Suppose a current I in a coil of N turns causes a flux  B to thread each turn The self-inductance L is defined by the equation Calculation of Self-Inductance Example: the Self-Inductance of a Solenoid

(b) Definition that describes the behaviour of an inductor in a circuit From Faraday’s Law of Induction The SI unit for inductance V s A -1 This is commonly called the henry (H) Hence in terms of the inductance and the current

Example: the Self-Inductance of a Toroid a b A cross section of a toroid Consider an elementary strip of area hdr r dr h

The Energy Stored by an Inductor I increasing  The energy dU supplied to the inductor during an infinitesimal time interval dt is: a b The total energy U supplied while the current increases from zero to a final value I is

Example: the energy stored in a solenoid Energy per unit volume (magnetic energy density) The equation is true for all magnetic field configurations

Mutual Inductance A changing current in coil 1 causes a changing flux in coil 2 inducing a voltage in coil 2:

Mutual Inductance It can be proved that the same value is obtained for M if one considers the flux threading the first coil when a current flows through the second coil (mutual inductance) (mutually induced voltages)

A Metal Detector Sinusoidally varying current Parallel to the magnetic field of C t

If a current I is established through each of the N windings of an inductor, a magnetic flux  B links those windings. The inductance L of the inductor is: A changing current I in a coil induces a voltage, where: Review and Summary An inductor with inductance L carrying current I has potential energy U: This potential energy is associated with the magnetic field of the inductor. In a vacuum, the magnetic energy per unit volume is

If two coils are near each other, a changing current in either coil can induce a voltage in the other. This mutual induction phenomenon is described by where M (measured in henries) is the mutual inductance for the coil arrangement