Mutual and Self Inductance: Magnetic Energy and R-L, L-C, L-R-C Circuits - Prof. Joseph Sl, Study notes of Physics

Download Mutual and Self Inductance: Magnetic Energy and R-L, L-C, L-R-C Circuits - Prof. Joseph Sl and more Study notes Physics in PDF only on Docsity! CHAPTER 30 SUMMARY Mutual inductance When a changing current 1i in one circuit causes a changing magnetic flux in a second circuit, an emf 2 is induced in the second circuit. Likewise, a changing current 2i in the second circuit induces an emf 1 in the first circuit. The mutual inductance M depends on the geometry of the two coils and the material between them. If the circuits are coils of wire with 1N and 2N turns, M can be expressed in terms of the average flux 2B through each turn of coil 2 that is caused by the current 1i in coil 1, or in terms of the average flux 1B through each turn of coil 1 that is caused by the current 2i in coil 2. The SI unit of mutual inductance is the henry, abbreviated H. (See Examples 30.1 and 30.2.) 1 2 di M dt  2 and 21 di M dt  2 (30.4) 2 2 1 1 1 2 B BN NM i i     (30.5) Self-inductance A changing current i in any circuit causes a self-induced emf   The inductance (or self-inductance) L depends on the geometry of the circuit and the material surrounding it. The inductance of a coil of N turns is related to the average flux B through each turn caused by the current i in the coil. An inductor is a circuit device, usually including a coil of wire, intended to have a substantial inductance. (See Examples 30.3 and 30.4.) di L dt  2 (30.7) BNL i   (30.6) Magnetic-field energy An inductor with inductance L carrying current I has energy U associated with the inductor’s magnetic field. The magnetic energy density u (energy per unit volume) is proportional to the square of the magnetic field magnitude. (See Examples 30.5 and 30.6.) 21 2 U LI (30.9) 2 02 B u   (in vacuum) (30.10) 2 2 B u   (30.11) (in a material with magnetic permeability  ) R-L circuits In a circuit containing a resistor ,R an inductor ,L and a source of emf, the growth and decay of current are exponential. The time constant  is the time required for the current to approach within a fraction 1/e of its final value. (See Examples 30.7 and 30.8.) L R   (30.16)