wuinduction2.ppt

Chap 28 inductance Self-Inductance Mutual Inductance Energy Stored in a Magnetic Field Key terms: mutual induction / inductance (互感/系数) self-induction / inductance (自感/系数) inductance (感应系数) Henry (亨利) transformer(变压器) inductor (电感器) 28-1 Self-Induction and Self-Inductance First Secondly Flash! Take a solenoid as an example, The back emf, induced in a coil when the current in that coil varies, is known as self-induction (自感). Such a coil is called an inductor. (电感器) What is the relationship of current to emf ? The relationship of current to emf is described by the self-inductance of the coil. (magnetic flux linkage) The magnetic field of the current solenoid: The magnetic flux through one loop: The induced emf in the solenoid: (emf in series) or, The coefficient L is defined as self-inductance (自感系数). So two definitions are given as A: cross-section of solenoid; l: length of solenoid; V: volume of solenoid. Notes: 1) L show the electric magnetic inertial of a loop 3) The “-” show emf is against the changing current 2) L depends on its own property. Geometry shape, size, number of turns etc. 4) N turns 5) SI Unit: Henry, 1H=1Wb/A Example: A toroid has a rectangular cross-section as shown in Fig. Show that the self-inductance is Where N is the total number of turns and r1, r2, and h are the dimensions shown in Fig. (P. 656) Solution: According to A. L. Example: A coaxial cable consists of thin coaxial cylinders of radii r1 and r2 (see the figure). The cylinders conduct equal current I in opposite directions. Obtain an expression for the inductance per unit length of the cable. By using Ampere’s loop law, we can easily get the magnetic field, The magnetic flux through an area of unit length A is given by By the inductance of an inductor, Solution: Example: A pair of straight parallel thin wires, such as a lamp cord, each of radius r, are a distance l apart and carry current to a