Faradays Law Faradays law cannot be derived from

Faraday’s Law Faraday’s law cannot be derived from the other fundamental principles we have studied Formal version of Faraday’s law: Sign: given by right hand rule Differential form of Faraday’s law:

Two Ways to Produce Changing Two ways to produce curly electric field: 1. Changing B 2. Changing A

Inductance Constant voltage – constant I, no curly electric field. Increase voltage: d. B/dt is not zero emf For long solenoid: Change current at rate d. I/dt: (one loop) emfbat R emfcoil

Inductance ENC emfbat R emfcoil EC Increasing I increasing B emfbat R L – inductance, or self-inductance emfind

Inductance ENC emfbat R L emfind EC Unit of inductance L: Henry = Volt. second/Ampere Increasing the current causes ENC to oppose this increase

Inductance: Decrease Current ENC EC emfbat R L emfind Conclusion: Inductance resists changes in current Orientation of emfind depends on sign of d. I/dt

Magnetic Field Energy Density? L I 2

Field Energy Density Electric and magnetic field energy density:

Current in RL Circuit If t is very long:

Current in RL Circuit If t is zero: Current in RL circuit:

Time Constant of an RL Circuit Current in RL circuit: Time constant: time in which exponential factor become 1/e

Current in an LC Circuit a=0

Current in an LC Circuit Current in an LC circuit Period: Frequency:

Non-ideal LC Circuit

Energy in an LC Circuit Initial energy stored in a capacitor: At time t=0: Q=Q 0 At time t= : Q=0 1/4 of a period System oscillates: energy is passed back and forth between electric and magnetic fields.

Energy in an LC Circuit What is maximum current? At time t=0: At time t= :

LC Circuit and Resonance Frequency: Radio receiver:

Two Bulbs Near a Solenoid Varying B is created by AC current in a solenoid What is the current in this circuit? Advantage of using AC: Currents and emf ‘s behave as sine and cosine waves.

Two Bulbs Near a Solenoid Add a thick wire: I 1 Loop 1: Loop 2: Node: I 2 Loop 2 I 3

Exercise