When British Prime Minister Gladstone met Michael Faraday, he asked him whether his work on electricity would be of any use. "Yes, sir" remarked Faraday with prescience, "One day you will tax it."

Induced electric fields, voltages Static E-fields begin or end on charges. But a changing B-field creates dynamic E-fields that loop around the changing B.

Induced electric fields, voltages These induced E-fields and voltages can drive currents in wires

Magnetic Flux through a coil or surface Here you would use only the area that has nonzero B to find flux

Faraday’s law Changing the magnetic flux through a coil creates an E-field that curls around the coil. This is just like adding a battery of voltage emf in the coil!

Lenz’ law is just an expression of what the minus sign means in: (-): The induced emf and E-field are in the direction that opposes the change in B-field or flux. (In loops, current flows to create a new B that tries to keep the flux the same)

What direction of current will be induced? The B field shown is weakened to zero in 2 seconds. If A = 0.5 m2, B = 3T, and N = 8 turns, what is the average induced emf? If the wire has a resistance of 4 W, what is the average induced current? You get the same effect if you rotate the coil by 90 degrees in a constant field. What direction of current will be induced?  

P1. The loop moves to the right into a region of B-field P1. The loop moves to the right into a region of B-field. At position b, the induced current in the loop is___ A. clockwise B. CCW C. zero P1. At position c, the induced current in the loop is___ P3. At position d, the induced current in the loop is___

Generators create “alternating” current (voltage), not “direct” (AC vs DC)

Hoover Dam generator Alternating Magnets NSNSNSNSNS on outside of “rotor” Fixed coils

The S pole of a magnet moves toward the loop. P4. The current induced in the coil is ____ viewed from the right side. Hint: the current opposes the magnet’s motion by creating a S pole facing it. A. clockwise B. counter clockwise Illustration

Motional emf A conductor contains mobile charges (we imagine them to be positive). If the rod moves with v, to which end will the + charges move? P4. A. top B. bottom + + Induced voltage across any moving conductor of length L + + +

Motional emf We could also analyze all our moving conductors via motional emf, instead of flux change. At what orientation of the loop does it creates the most emf?

Eddy currents When a metal moves in a B-field, or a magnet moves over a metal, currents are induced inside (fighting the change), and energy is lost to resistive heating: it feels drag.

P5. If the current in the long straight wire is decreasing, the current induced in the coil is A. clockwise B. counter clockwise P6. If we close the switch, the current induced in the coil at the right is If after a long time we open the switch, the current induced in the coil is______

Technologies you can now understand: Guitar pickups RF ID Cards