1. Electromagnetic induction
Objectives:
Describe what happens when a coil of wire is placed in a changing magnetic field.
Calculate the magnetic flux.
Calculate the induced EMF in a coil or a straight conductor.
Determine the direction of the induced current by applying Lenz’s law.

2. Electromagnetic induction
is the production of a potential difference (voltage) across a conductor when it is exposed to a varying magnetic field.
Discovery was credited to Michael Faraday.
Faraday’s law of electromagnetic induction states that any change in the magnetic environment of a coil of wire will cause a voltage (EMF) to be "induced" in the coil.

3. Magnetic flux
is the product of the average magnetic field times the perpendicular area that it penetrates.
= ABcos
= magnetic flux in T·m2
A = area of the coil in m2
B = magnetic field in T
= angle between B and the area vector(an arrow drawn perpendicular to the plane of the coil)
Note: magnetic flux is also measured in Weber (Wb)
1 Wb = 1 Tm2

4.  B
 is the angle between B and the area vector (red arrow)

5. Induced EMF in a Coil  = - N  t = - N (f - i)
= - N(AfBfcosf – AiBicosi)
 = induced electromotive force in V
N = number of turns in the coil
A= area of the coil in m2
B = magnetic field
= magnetic flux in T·m2
t = time is takes for the flux to change

6. What is the angle Φ?
The field is perpendicular to the plane of the coil (Φ=0°)
The field of parallel to the plane of the coil (Φ=90°)
The normal to the coil is perpendicular to the field (Φ=90°)
The normal to the coil is parallel to the field (Φ=0°)
The plane of the coil makes an angle θ with the filed (Φ=θ+90°)

7. Lenz’s law
Remember the negative sign in the equation  = - N  ? t The sign is explained by Lenz’s law.

8. Lenz’s law
When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant.

9. Lenz’s law
Just as mass resists changes to its velocity, conducting hoops resist changes to the magnetic flux through them by creating their own flux to minimize the change.

11. Lenz’s law example
Determine the direction of the current in the loop: X X X X X X Bin is increasing

12. Answer Counter-clockwise
Since the magnetic field is increasing in the direction into the page, the coil will create magnetic field that is directed out of the page to counter the change in the flux inside the coil.
Using the second right hand rule, grab the coil such that your fingers are pointing the direction of the magnetic field (created by the coil) inside the coil and your thumb points to the direction of the current.

13. Lenz’s law example
Determine the direction of the current in the loop: X X X X X X Bin is decreasing

14. Answer
Clockwise
Since the magnetic field that is directed into the page is decreasing, the coil will create more magnetic field into the page to resist the decrease of the field into the page.
Using the second right hand rule, grab the coil such that your fingers (magnetic field) are pointing into the page inside the coil. Your thumb (current) will then be pointing in the clockwise direction.

15. Lenz’s law example
Determine the direction of the current in the loop: Bout is increasing

16. Answer
Clockwise
Since the magnetic field is increasing out of the field, the loop will create a magnetic field into the page to resist the change.
Using the second right hand rule, the fingers will point into the page inside the loop so the thumb is pointing in the clockwise direction.

17. Lenz’s law example
Determine the direction of the current in the loop: Bout is decreasing

18. Answer Counter-clockwise
Since the magnetic field is decreasing out of the page, then the coil will create additional magnetic field out of the page to resist the decrease.
Using the right hand rule, the fingers point out of the page inside the coil so the thumb is pointing counter-clockwise.

19. Lenz’s law example Determine the direction of the current in the loop:
i increasing

20. Answer Counter-clockwise
The magnetic field inside the loop due to the current in the vertical wire is increasing into the page. So the loop will create magnetic field inside the loop that is directed out of the page.
With fingers pointing out of the page inside the loop, the thumb points in the counter-clockwise direction.

21. Lenz’s law example Determine the direction of the current in the loop:
i decreasing

22. Answer
Clockwise
The magnetic field inside the loop due to the current in the vertical wire is decreasing into the page. The loop will then create more field into the page.
Using the second right hand rule, fingers are pointing into the page inside the coil so the thumb is in the clockwise direction.

23. Motional emf
 = BLv  = induced electromotive force in V B = magnetic field in T L = length of the conductor in m v = speed of the conductor in m/s

24. Motional emf
x x x x x x B(in) x x x x x x x x x x v x

25. Motional emf
The rod has no net charge, but conduction electrons within the rod are free to move. First, assume that these electrons are moving through the field with the velocity of the rod. Apply the right-hand rule to determine the direction of the force these electrons experience.

26. Motional emf
A conducting rod moving in a magnetic field acts like a battery, because of the separation of charge from the magnetic force acting on the rod’s conduction electrons.