I really don’t like the order in which your author presents the material in this chapter, so I’m going put in a slightly different order.
Introduction:
Recall what the Biot-Savart Law and, more generally, Ampere’s Law say:
“Electric Currents Create Magnetic Fields”
PhET EM
Also, remember this was discovered accidentally by Oersted in 1819.
For some years after, people wondered about the inverse of this process:
“Can Magnetic Fields Create Currents?”
PhET coil
If the magnet and the coil just sit there, then there is no current.
In 1831, Michael Faraday (English) and Joseph Henry (American) made another accidental discovery.
PhET trans
Turning the current on and off in one coil induces a current in the other.
How are the two coils connected? By a Magnetic Field.

Faraday went on to thoroughly study this to find what aspect of the magnetic field can induce a current in a loop.
Mag & coil
Experiment: Observations:
1.) Magnet and coil motionless: No Current
2.) Magnet moving toward the coil: Current in one direction
Magnet moving away from the coil: Current in the opposite direction
Reversing the polarity of the magnet reverses the direction of the current.
3.) Coil moving toward the magnet: Current in one direction
Coil moving away from the magnet: Current in the opposite direction
This case is not surprising. Here, we have charges moving in a magnetic field, so they will feel a force. This is called “Motional EMF.”
However observation #2 above can’t be explained as motional EMF.
4.) Two coils with one switched on and off Brief Current PhET trans

Faraday realized that all of these experiments have one feature in common:
“There is an induced current in the light bulb coil when
the magnetic field through the coil is changing .”
Faraday was also able to deduce a quantitative description of this:
Faraday’s Law:
Conducting Loop with
resistance R
The Induced EMF* in the Loop is:
The Induced EMF then causes an Induced Current:
*The absolute value signs are there because Faraday’s Law in this form doesn’t tell us anything
about the direction of the induced EMF or current; for that we’ll need Lenz’s Law (coming soon).

Back in chapter 27, we used the flux of the electric field in our work with
Gauss’ Law.
Everything that we learned about the electric flux there also applies to the magnetic flux here. All we have to do is:
Then all of the equations and the ways we calculated the flux of the electric field in chapter 27 will work for flux of the magnetic field as well.
The following two slides are the exact same slides that we used in chapter 27 but changed to the magnetic flux using the above replacements:

Flux is a measure of how much a magnetic field passes through a 2D surface.
Flux depends on the size and direction of the field and the size, shape, and orientation of the surface .
Your author starts with flux for special cases and builds to a general definition;
read his account, we’ll do the opposite:
Flux for the General Case
(any field, any surface)
Magnetic Flux:
2D surface
Element of area
(New, different for magnetic!)
Note: this is called a surface integral

Uniform Magnetic Field & Planar Surface:
Uniform Magnetic Field & Planar Surface perpendicular to the field:
For either of these cases, the relation to remember is:

Using the group’s computer , one of you log onto masteringphysics and begin the exercise: PhET Faraday’s Law .
Use the computer to complete the exercise, but record your answers on the sheet to hand in – that’s what will be graded.
When you’re done with the exercise, make sure your Group’s name and all of your names are on it, and turn it in. Feel free to play with the simulation if you have time.
Anytime you want play with the PhET simulations, just go to: http://phet.colorado.edu/

The induced EMF:
And the magnetic flux is:
Where S is the surface of the conducting loop.
Faraday’s Law says:
“The induced EMF is given by the rate
at which the magnetic flux is changing.”
What can produce a changing flux?
Any of these can occur simultaneously – we’ll see problems like that!
*By the way: Faraday’s Law is our 4 th Maxwell Equation, but we’ll want to write it in
a different form on Monday.

A 1000-turn coil of wire has a diameter of 1.0 cm and is in a uniform magnetic field that increases from 0.1 T to 0.3 T in 10 ms. The axis of the coil is parallel to the field.
What is the EMF in the coil? (LC)
Your sketch should look like this:
N = 1000 turns
(i.e. loops)

The loop in the figure is being pushed into the 0.2 T magnetic field at 50 m/s.
The resistance of the loop is 0.1 Ohms.
What are the magnitude and direction of the current in the loop?
(LC, magnitude)
How can you figure out which way the induced current goes,
clockwise or counterclockwise?

Faraday’s Law:
Conducting Loop
with resistance R
Lenz’s Law can be used to find the direction of the induced current:
This is a very odd physical law – no equations, just words.
The most important step in applying Lenz’s Law is to ask:
“What is the Flux doing, increasing or decreasing?”
Let’s go back to Problem WB33-2 and figure out which way the induced current goes.

The figures below show a 10 cm diameter loop in a magnetic field.
The loop’s resistance is 0.20 Ohms. What are the magnitude and direction (LC: CW or CCW) of the induced current in the loop?
(LC: CW or CCW) (LC: CW or CCW) (LC: CW or CCW)

A 100 turn coil with a diameter of 2.0 cm and resistance 0.1 Ohm is at rest in a horizontal plane. A uniform magnetic field 60 o away from the vertical increases from 0.5 T to 1.5 T in 0.60 s. a) What is the induced current in the loop? (LC) b) What is the direction of the current looking down
from the vertical (CW or CCW)? (LC)