Electromagnetic Induction -------------------------------------------- Joseph F. Alward, PhD     Department of  Physics   University of the Pacific

A transformer substation

 Important Equations and Concepts                        

(1)    Induced emf =  vBL (2)     F = IBL (3)    F  = BA cos q (4)    Induced emf =  N DF/Dt ---------------------------------------- Important Mathematical Relationship: D(FG) = (DF)G    if G = constant

Faraday's Law:  A changing magetic flux through a  loop or loops of wire induces an  electromotive force (voltage) in each  loop. ----------------------------------------------------- Lenz's Law: The induced current sets up a magnetic field which opposes the cause of the induced current.

 Voltage in Wires Moving in Magnetic Fields   

Charges at ends of rod exert electrostatic force on any charge q in rod.

At equilibrium,  Fe = Fm             (1) qE = Fm              (2) qE = qvB            (3)   E = vB              (4) Recall, E =  DV /Ds        (5) DV= E Ds           (6)      = vBL             (7) (induced emf) DV = vBL

  Magnetic Force on Induced Current                

Magnetic force to the left resists push to the right by the hand.

F = IBL

 Space Shuttle:  Magnetic Forces on Induced Currents    

DV = vBL        = 3467 volts Magnetic force F = IBL on tether caused orbit to decay.

 
 Magnetic Force on Induced Current                     

Rod falls down along frictionless tracks with ever-increasing speed v.

Hypothetical positive charges are falling down with the rod.   Point thumb down.

F = IBL Upward magnetic force balances the pull by the Earth. Terminal speed is reached

 
  A Current Generator                                                          

Electron is moving down.

F = qvB (Reverse direction because charge is negative.)

 The First Generator                                                                  

Michael Faraday   (1791-1867)

 Christmas Lecture                   

 Magnetic Flux                                                               

F = BA

F  = BA cos q

  Changing Flux              

Wire is pulled to the right by an unseen force.               Induced emf = vBL

  Changing Flux and Faraday's Law            

F = BA                 (1) DF = D(BA)            (2)        = BDA               (3)        = B(LDx)           (4)

DF/Dt  = BLDx /Dt      (5)              = BLv              (6) ---------------------------  Faraday's Law:   The induced emf in a single coil of wire is                                                  DF/Dt

    Faraday's Law        

If there is a stack of N loops of wire, then the induced emf is N times as great:                         Induced emf  =  NDF/Dt

  Faraday's Law Example                                                                        

Induced emf = DF/D t                            F = BA

This time, DF changes because the B-field changes. DF = (DB)A                         ---------------------------------- Example:  B0 = 0.04 T                                 B  = 0.07 T                 DB  = 0.03 T                    A = 0.004 m2                   Dt = 0.005 s                 DF = (0.03)(0.004)                        = 1.2 x 10-3 T-m2 Induced emf = DF/Dt                     = 1.2 x 10-3 /0.005                     = 0.24 V

   Faraday's Law Examples                  

Flux through coil changes because bar magnet is moved up and down.

AC current in bottom coil causes changing B-field along iron core.

  Flux Changing by Changing Areas               

Induced emf = N DF/Dt     (Omitting negative sign)

F = BA                    (1) DF = B (DA)          (2) Magnetic field doesn't change; area changes. The more quickly the loop is stretched, the smaller will be Dt and the larger will be the transient emf.

 Changing Magnetic Fields Cause Changing Flux       

This is the field of the                                                       induced current.

DF changes in this case because the magnet is brought closer to the loop; consequently, more B arrows penetrate the plane |of the loop. Flux F increases. Induced emf = N DF/Dt

  Changing Magnetic Fields                      

This is the field of the                                                      induced current.

Magnet is removed from the loop; consequently, fewer B arrows penetrate the plane|of the loop. Flux F decreases. Induced emf = N DF/Dt .

   Stealing Power

 Radio Antenna           

 Radio Antenna Uses Faraday's Law 

Radio waves are electromagnetic.  The oscillationg B-field of the EM waves induce an emf in the coil.

   The Induction Stove                                 

A changing flux through the bottom of the metal pot generates an emf which causes current to circulate around the bottom of the pot. I2R heat is dissipated in metal pot, but not in the glass pot or the stove top because they're insulators.

 Ground Faults                                                                               

Current takes shorter path to ground by going through hand, arm and legs of the person. A properly grounded wire will prevent this. Faulty grounding can be overcome by a "ground-fault circuit interrupter"   (GFCI or GFI)

 Ground Fault Circuit Interrupter        

(detail follows) 

 Ground Fault Circuit Interrupters Explained                      

Net current through iron ring is zero unless there's a short in the circuit. If the return current is less than the entering current, a magnetic field will be suddenly be created in the iron ring, and this changing field will induce an emf in the sensing coil. .

  Electric Guitar's Pick-Up Coil                                                   

Vibrating string changes flux through coil, inducing an emf which oscillates in rythym with the guitar string.

 PlayBack Read Head in a Tape Player -- Moving Coil Microphone                   

Iron core becomes magnetized, causing the flux through the coil to change.

Fluctuating air pressure moves diaphragm with coil attached alternately toward and away from magnet.

 Writing Data on Magnetic Disk

 Lenz's Law                                                                                                        

Magnet is brought closer, increasing the number of       B-field penetrations of the plane of the loop.

Cause:  Magnet moving to the right Effect:  Coil becomes an electromagnet              to oppose movement of bar. Rule:  "see counterclockwise, see north" ----------------------------------------- Another way to look at it: Cause:  More B-arrows puncture plane Effect:  Induced electromagnet creates              its own B-field arrows pointing              in the opposite direction, partially              cancelling the increase.

   Lenz's Law                                                                                          

Magnet is taken away from the loop, decreasing the number of B-field penetrations of the plane of the loop.

Cause:  Magnet moving  away, to the left Effect:  Coil becomes an electromagnet  to attract back the bar magnet. Rule:  "see clockwise, see south" ----------------------------------------- Another way to look at it: Cause:  Fewer B-arrows puncture plane Effect:  Induced electromagnet creates  its own B-field arrows pointing in the  same direction as the bar magnet's field,  partially cancelling the loss of B arrows.

   Lenz's Law                                                                                          

Cause:  Increase in flux Effect:   Induced current in loop creates a magnetic             field (not shown) which partially cancels flux

A second way to look at it: The induced current as viewed from the left is clockwise, making the left face of loop the south pole, which is repelled by the south pole of the electromagnet. (Effect opposes cause.) ---------------------------------------------- A third way: Growth of counter-clockwise current is opposed by growth of clockwise current.

   Jumping Ring

If current is suddenly established in the coil,   what will happen to the ring, and why?

   Lenz's Law                                                                                             

Cause:  Decrease in flux Effect:   Induced current in loop              creates a magnetic f ield              (not shown) which               partially restores flux

 Lenz's Law                                                                                                      

"See counterclockwise, see north" --------------------------------------- Ring on left acts like a magnet with a north face on top to repel the falling magnet (effect opposing cause) As viewed from above is current in ring clockwise, or counter-clockwise? --------------------------------------- What happens in the split ring?

  Lenz's Law                                                        

Cause:  bar magnet moving away. Effect:  induced electromagnet's polarity will be such that it will try to attract the magnet back. What will be the polarity, north, or south, of the left face of the induced electromagnet?

  Lenz's Law                   

Current is suddenly established in wire at bottom.  What is the direction--clockwise, or counterclockwise--in the loop?

 Lenz's Law                                                      

What will be the direction of the current in the resistor when the switch is closed?  Hint:  what will be the polarity of the right face of the first magnet?

  Faraday's and Lenz's Laws           

An emf is generated only if the flux is changing. Note that current is zero while the loop is completely inside the magnetic field.

 Toroid Choke

A sudden surge in current is partially choked off by the "back emf" induced when the magnetic flux through the loop suddenly changes. The flux change is multliplied by the presence of the soft-iron cylinder surrounding the wire.

   AC Generator Explained                         

Electrons in opposite sides of loop are moving  in opposite directions, so the forces on them areoppositely directed. A half-cycle later, those electrons are moving in the opposite direction.

  Electric Generator                     

This is what's inside:

 Counter Torque                                                                  

  Principles of Transformer Action                

   Iron Core Transformer                  

This is a "step-up" transformer because the voltage is increased.

  Power Transmission and Transformers                      

Output power = IV -------------------- Why is output at low current and high voltage, and not high current and low voltage? -------------------- Answer:  I2R losses

   Automobile Ignition System                                  

Spark plug gap is about 1/50 inch (0.020 in), or about 1/20 cm. Breakdown strength of air is 30,000 V/cm, so 1500 V is required across the 1/20 cm spark plug gap. If there are 1000 turns on the primary, how many turns must the secondary have?

   Transformer Station and Telephone Pole Transformer 

Steps down from 240,000 V to 8000 V

Steps down from 8000 V to 240 V