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 (κ m >>1, κ 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 ΔV R =-iR   =L/R =L/R inductive time constant t=0, i=0 t→∞, i=ε/R.

RC Circuits Combine Resistor and Capacitor in Series C  a R b Switch at position (b) LR Circuits ΔV R =iR  t=0, i=0 t→∞, i=ε/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 ΔV 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