1. Magnetic Flux
()
is related to the number of magnetic field lines passing through a surface B N S B
Magnetic Flux =  = B A cos 
SI unit = 1 Weber = T·m2
B = magnetic field
A = surface area
 = angle between B and the Normal to the surface

3.  = BA The field strength tells us how much flux passes through 1m2.
It tells us how close the lines are.
If 4 lines pass through each m2 then how many lines pass through 4m2

4. Lenz’s Law
The induced current in a circuit will produce a magnetic field to cancel the original change in flux that caused the induced current in the first place.
Imagine a closed loop of wire at rest and perpendicular to this slide where no external magnetic field is present.
I (induced) B
B (induced)
Because the flux changed through the loop, current flows in the loop while the flux changes…but in which direction?
Now imagine that a uniform magnetic field directed to the right develops, and passes through the loop. The magnetic flux increases in the loop to the right.
The induced current must flow in a direction to produce a magnetic field to oppose the original change in flux. In this case, the current must be in the direction shown (right hand rule) to produce a magnetic field to the left.

5. The induced current in a circuit will produce a magnetic field to cancel the original change in flux that caused the induced current in the first place.
Once the change in flux stops, that is, once the magnetic field is constant through the loop, then induced current stops.
I (induced)
I (induced) B
B (induced)
B (induced)
If the magnetic field strength were to decrease, then the flux through the circuit would decrease, and current would be induced again.
The induced current would flow in the opposite direction because it will produce a magnetic field to cancel the change in magnetic flux.

6. As the loop is pulled and its area is decreased, what is the direction of the current that is induced in it?

7. Magnetic flux in the loop increases
Counterclockwise

8. Magnetic flux in the loop increases
Clockwise

9. Magnetic flux in the loop decreases
Clockwise

10. Magnetic flux in the loop decreases
Counterclockwise

13. One can also induce current in a circuit by moving a wire through an external magnetic field so that the flux through the loop changes.
x x x x
B into page F F I I
Since energy is conserved the kinetic energy of the wire must decrease
because some of the its energy is being used to move electrons in the
wires. But why would the wire lose speed for no apparent reason?
Let’s imagine that the loop is going to move with constant speed as it
passes through the magnetic field.
As the loop exits the magnetic field, the flux into the page changes
again. The induced current in the left hand vertical wire experiences
magnetic force to the left (right hand rule), and acts to slow the wire
down a second time.
As the loop enters the field, however, current begins to flow because
the flux is changing. The initial energy of the system was just the KE of
the wire loop, but now the electrons in the wire are moving and this
takes energy too.
There is a very good reason for the wire to lose speed. When current
flows up through the right hand vertical wire, magnetic force pushes
that wire to the left (review right hand rules for FMAG on a wire).
As the entire loop moves through the field no current is induced during
because the magnetic flux through the loop is constant. No magnetic
forces retard the loop so it moves with constant speed to the right.

14. Let’s go through those methods of inducing voltage.
1. Change the magnetic field strength that passes through the circuit.
x x x
Imagine a region in which a uniform magnetic field exists, and is directed into the page shown by the x’s.
Now imagine that there is a loop of wire in that field so that the field lines pass through it.
x x x x
B into page
As long as the external magnetic field remains constant, no current is induced in the loop because the flux is constant. I I
If the magnetic field increases (into the page), then the flux will increase and current will be induced in the loop as shown while the flux is increasing.
If the magnetic field were to decrease back to its original intensity, then the flux will decrease and current will be induced in the loop in the opposite direction as shown while the flux is decreasing.

15. Let’s go through those methods of inducing voltage.
2. Change the area of the loop in the magnetic field.
If the area of the loop in the magnetic field is somehow made larger, then the flux through the loop will increase. This will induce the current shown while the flux is increasing.
If both the area of the loop and the strength of the magnetic field remain constant, the flux will remain constant and no current will be induced.
x x x x
B into page
If the area of the loop in the magnetic field is reduced, either by returning to its original size or by shrinking further, then the flux through the loop will decrease. This will induce the current shown while the flux is decreasing. I I

16. Let’s go through those methods of inducing voltage.
Move the loop through the external field so that its area in the field
changes, or rotate the loop in the external field so the angle between the field and the face of the loop changes to change the flux.
x x x x
B into page I I
The square wire loop is just outside of the region of the magnetic field
directed into the page. The flux through the loop is zero at this time,
but the loop is about to begin moving to the right.
As the loop enters the field, the flux through it increases. While the flux
is increasing, current develops in the loop as shown.
Assuming the wire loop has resistance R…
ΔV = I R
-B L v = I R the current, I, induced is
I = - B L v/R
When the flux was changing…
ΔV = - ΔΦ / Δt = - B (ΔA) / Δt ΔA = L·Δx
ΔV = - B (L·Δx) / Δt the speed, v = Δx/Δt
ΔV = - B L v
As the loop exits the magnetic field, the flux through the loop changes
again. This time it decreases because there are fewer filed lines passing
through the loop (area is decreasing). While the flux is decreasing,
current develops in the loop as shown above.
Once the loop moves entirely into the field, then flux through it is
constant because both the field strength and the area of the loop in the
field is uniform. No current is induced during this time.
We can determine the amount of voltage and current induced as the
loop entered and exited the magnetic field in terms of the variables:
Side length of loop = L, speed of loop = v, external magnetic field = B

19. Simple Model of a Generator
Which way will the current flow through the conductor as the conductor moves up along the metal bars?  
No current
Can’t be determined