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”

Various ways of making changing magnetic field Change current through the solenoid Time varying B can be produced by moving coil: by moving magnet: move coil – get changing B and curly E How to create a time-varying magnetic field? by rotating magnet: (or coil)

Clicker Solenoid has circumference 10 cm. The current I1 is increasing causing increasing B1 as in the figure. Solenoid is surrounded by a wire with finite resistance. When length of the wire is changed from 30 to 20 cm what will happen to detected current? It will decrease Increase Does not change ammeter + - B

A Circuit Surrounding a Solenoid Example: B1 changes from 0.1 to 0.7 T in 0.2 seconds; area=3 cm2. Application of Faraday’s law Circuit acts as battery. What is the ammeter reading? (resistance of ammeter+wire is 0.5)

Clicker: A Circuit Not Surrounding a Solenoid If we increase current through solenoid what will be ammeter reading? positive current negative current zero zero

Voltmeter Reading Voltmeter will read emf. Be careful using voltmeter when AC currents are present. Problem – when measuring dV keep wires which go to Voltmeter so that they do not encircle area with changing B Voltmeter = ammeter with large resistance

The EMF for a Coil With Multiple Loops Each loop is subject to similar magnetic field  emf of loops in series: Series connection of many loops with the same emf

Exercise 1. A bar magnet is moved toward a coil. What is the ammeter reading (+/-)? 2. The bar magnet is moved away from the coil. What will ammeter read? S side in = B –field increasing and points to the left, to opposes the change current should run CW – positive current into (+) side of voltmeter move coil – get changing B and curly E Positive Negative

Clicker 2

Faraday’s Law and Motional EMF ‘Magnetic force’ approach: I Use Faraday law: When a wire moves through magnetic field -> magnetic forces drive current through wire I

Faraday’s Law and Generator I Old problem

Exercise A uniform time-independent magnetic field B=3 T points 30o to the normal of the rectangular loop. The loop moves at constant speed v 1. What is the emf? 2. In 0.1 s the loop is stretched to be 0.12 m by 0.22 m. What is average emf during this time? Old problem

Two Ways to Produce Changing  Two ways to produce curly electric field: 1. Changing B 2. Changing A Changing B field or area (shape, orientation)

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

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