Chapter 23 Faraday’s Law

Faraday’s Law Michael Faraday (1791 - 1867) Faraday’s law cannot be derived from the other fundamental principles we have studied Formal version of Faraday’s law: Unlike motional emf – Faraday cannot be derived . A British physicist and chemist, he is best known for his discoveries of electro-magnetic rotation, electro-magnetic induction and the dynamo. Faraday's ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a magnetic field should be able to produce an electric current. He demonstrated this principle of induction in 1831. Faraday expressed the electric current induced in the wire in terms of the number of lines of force that are cut by the wire. The principle of induction was a landmark in applied science, for it made possible the dynamo, or generator, which produces electricity by mechanical means Sign: given by right hand rule “Current opposes change in B”

Clicker 2

Inductance Constant voltage – constant I, no curly electric field. Increase voltage: dB/dt is not zero  emf For long solenoid: Change current at rate dI/dt: One factor of N from B field of solenoid, other factor due to changing flux through the N loops. (one loop) emfbat R emfcoil

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

Inductance ENC R L emfbat EC emfind Unit of inductance L: American physicist Joseph Henry, in 1831 discovered the effect of time-varying magnetic field simultaneously with Michael Faraday. Unit of inductance L: Henry = Volt.second/Ampere Increasing the current causes ENC to oppose this increase

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

Transformer Magnetic core conducts magnetic flux. Energy conservation:

Magnetic Field Energy Density Is there energy stored in magnetic field? Did it for capacitor. Now can show that there is an energy density associated with magnetic field by expressing the energy in an inductor in terms of the magnetic field.

Field Energy Density Electric and magnetic field energy density:

Current in RL Circuit Last shown. 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 drops e times

Classical Theory of Electromagnetic Radiation Chapter 24 Classical Theory of Electromagnetic Radiation

Maxwell’s Equations Four equations: Gauss’s law for electricity Gauss’s law for magnetism Faraday’s law Ampere’s law for magnetism (incomplete) Provide a complete description of possible spatial patterns of electric and magnetic field in space.

Ampere’s Law Charging a capacitor: Current inside No current inside Lets work with the last one… Grey area soap film is stretched flat over the circular Ampere’s path.

Maxwell’s Approach Time varying magnetic field leads to curly electric field. Time varying electric field leads to curly magnetic field? I Current in wire I – causes change in E flux, should cause the same effect in curly B ‘equivalent’ current combine with current in Ampere’s law

The Ampere-Maxwell Law Works! This law cannot be derived, but all experimental facts prove it, especially phenomena of radio and light-waves

Maxwell’s Equations Four equations (integral form) : Gauss’s law Gauss’s law for magnetism Faraday’s law Ampere-Maxwell law Add Lorentz to complete the list of fundamental equations of electricity and magnetism Lorentz eq – defines the meaning of electric and magnetic field in terms of their effect on charge + Lorentz force