1. Chapter 29

2. Electromagnetic Induction
We know
Current loop + magnetic field  torque
But does a
Torque + magnetic field  current?

3. Faraday’s Law The circle represents the current in the loop.
How to get more current
Use two magnets
Make loop larger
Make magnet faster
So the more field lines which move through the coil are what causes the current
Recall

4. Faraday’s Law Cont’d
The induced EMF in a closed loop equals the negative time-rate of change of the magnetic field.
But what is EMF?

5. EMF—Electromotive Force
Any chemical, solar, mechanical, heat method of creating a potential difference
Batteries
Alternator, dynamo
Solarcell, photovoltaic
Thermocouple
Symbol E
Units: volts

6. But what is the direction?
Binduced
Binduced
The circle represents the current in the loop.
Lenz’s Law:
The direction of any magnetic induction effect is such as to oppose the cause of the effect.

7. Mathematically,
The magnetic flux is the sum of the magnetic field lines going through an area. It changes with time if:
The magnetic field varies with time
The area of the loop varies with time
The angle that B makes with the normal of the surface of dA varies with time
The “minus” sign is to show that the EMF acts to oppose the magnetic field generating it.
SI unit for magnetic flux is weber = 1 T*m2

8. 3 Ways to Change the Flux Move the Magnet Grow/Shrink the Ring
Spin the Magnet or Spin the coil

9. Faraday’s Law Direction Rules
Define the normal to the area under consideration as positive (A is positive)
From Faraday’s Law, find the sign of the flux, F, and the sign of its rate of change, d F /dt
If flux increasing, d F /dt>0
If flux decreasing, d F /dt<0
Since EMF=-(d F /dt), then
d F /dt>0 implies EMF<0
d F /dt>0 implies EMF>0
Point thumb of right hand
In negative direction if EMF<0
In positive direction if EMF>0
Your fingers of your RH are now pointing in the direction of current.

10. Electric Guitar Induced Magnetic Field on String String S N S V N
Permanent Magnet

11. Slide Wire Generator v Area=x*L But X X X X X X X X X X X X X X
v=dx/dt
d(area)/dt=vL
X X X X X X X X X X X X X X L R
EMF=dF/dt=B*d(area)/dt
EMF=BvL
B into page
EMF=iR
i=EMF/R = BvL/R
P=(EMF)*I
P=B2v2L2/R

12. Hey, wait a minute, we created a current, so that must mean there is now an electric field!
But the induced current is moving in a circle so
So a time varying magnetic creates an electric field with no divergence

13. But earlier, you said Yes, but that was for ELECTROSTATIC situations
Now the charges are moving!
Electric potential has meaning only for electric fields produced by static charges. It has no meaning for electric fields produced by induction

14. Recall
So it should surprise you that the closed path integral of the magnetic field is
Note the difference in signs so for similar situations, the curl of the B field will be opposite the curl of the E field
In order to keep things straight in his own mind, Maxwell called this
a “displacement current”. He could then use Ampere’s law

15. Displacement Current Maxwell’s fictional current -q +q i i id
This plate induces a negative charge here
Which means the positive charge carriers are moving here
and thus a positive current moving to the right

16. Maxwell’s Equations
The electric field spreads into space proportional to the amount of static charge and how closely you space the static charges
Magnetic field lines are closed loops and always return to the source creating them
An electric field, resembling a magnetic field in shape, can be created by a time-varying magnetic field.
There are two ways to produce a magnetic field: 1) by a current and 2) by a time-varying electric field.