Chapter 23 Faraday’s Law

Faraday’s Experimentation Set wire (connected to ammeter) around a solenoid. Can a current be observed in this wire?

Solenoid: inside outside Constant current: there will be no forces on charges outside (B=0, E=0) What if current is not constant in time? Let B increase in time E~dB/dt Non-Coulomb E NC ! Changing Magnetic Field

1. Coulomb electric field: produced by charges 2. Non-Coulomb electric field: using changing magnetic field Same effect on charges: Two Ways to Produce Electric Field Field outside of solenoid

Right hand rule: Thumb in direction of fingers: E NC Exercise: Magnetic field points down from the ceiling and is increasing. What is the direction of E? Direction of the Curly Electric Field “Current opposes change in B”

E NC causes current to run along the ring What is emf and I? Driving Current by Changing B Ring has resistance, R

1. Change radius r 2 by a factor of 2. emf does not depend on radius of the ring! 2. One can easily show that emf will be the same for any circuit surrounding the solenoid Effect of the Ring Geometry

=0 for any path which does not enclose the solenoid! Round-Trip Not Encircling the Solenoid

Is there current in these circuits? Exercise

Can observe experimentally: I=emf/RE NC ~emf 1. E NC ~dB/dt 2. E NC ~ cross-section of a solenoid Quantitative Relationship Between B and EMF

-magnetic flux  mag on the area encircled by the circuit (wire loop) Magnetic flux on a small area  A: Definition of magnetic flux: Magnetic Flux This area does not enclose a volume!

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 Michael Faraday ( ) Faraday’s Law “Current opposes change in B”

Time varying B can be produced by moving coil: by moving magnet:by rotating magnet: (or coil) Various ways of making changing magnetic field Change current through the solenoid

Clicker ammeter Solenoid has circumference 10 cm. The current I 1 is increasing causing increasing B 1 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? A.It will decrease B.Increase C.Does not change + -

Example: B 1 changes from 0.1 to 0.7 T in 0.2 seconds; area=3 cm 2. What is the ammeter reading? (resistance of ammeter+wire is 0.5  ) A Circuit Surrounding a Solenoid

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

Each loop is subject to similar magnetic field  emf of loops in series: The EMF for a Coil With Multiple Loops

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? Exercise

‘Magnetic force’ approach: I Use Faraday law: I Faraday’s Law and Motional EMF

I Faraday’s Law and Generator

A uniform time-independent magnetic field B=3 T points 30 o 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? Exercise

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