Chapter 36 Inductance Capacitance Electric energy Magnetic energy Inductance Calculating the capacitance Procedure: 1.Suppose that the capacitor is charged, with q on the two plates respectively. 2. Find the electric field E in the region between the plates. 3. Evaluate the potential difference between the positive and negative plates, by using the formula: 4.The expected capacitance is then: Calculating the Inductance Procedure: 1.Suppose i 2. Find the magnetic field B, B 3. Evaluate the EMF by using the formula: Calculating the Inductance L is independent of i and depends only on the geometry of the device. a b Calculating the Inductance Calculating the capacitance a b Inductance of a Toroid Inductors with Magnetic Materials Ferromagnetic cores ( m >>1, m = ) provide the means to obtain large inductances. RC Circuits Combine Resistor and Capacitor in Series C a R b Switch at position (a)(b) LR Circuits RC Circuits Combine Resistor and Capacitor in Series C a R b Switch at position (a) LR Circuits V R =-iR =L/R =L/R inductive time constant t=0, i=0 t, i=/R. RC Circuits Combine Resistor and Capacitor in Series C a R b Switch at position (b) LR Circuits V R =iR t=0, i=0 t, i=/R. =L/R =L/R L-C circuit Electric energyMagnetic energy Energy conservation Damped and Forced oscillations If there are resistances in circuit, the U is no longer constant. Resonance Energy Storage in a Magnetic Field V R =-iR i= (dq/dt)= ( dq)/dt, the power by the emf device. i 2 R, the power consuming in the resistor. Li(di/dt), the rate at which energy is stored in the space of the inductor, it can be put out, when switch to b energy is stored in the electric field energy is stored in the magnetic field inductance i UBUB i magnetic field UBUB Analogy to Simple Harmonic Motion kxU s mvK C q U E LiU B Electric FieldMagnetic Field Electric FieldMagnetic Field Electric FieldMagnetic Field Gauss Law Ampere Law Electric FieldMagnetic Field Induction Electric FieldMagnetic Field Electric FieldMagnetic Field Example a b a b Exercises P , 10, 23, 41 Problems P842 3, 5