1. Electromagnetic Induction
Electricity from Magnetism

2. Induced Current
When a conductor is moved in a magnetic field, current can be induced (caused)
Faraday’s Original Experiment

3. Many Ways to Produce EMF
Many forms of changing magnetic field can produce Emf (current)
Magnet or coil or both can move
Field can turn on or off due to closing or opening a switch

4. Faraday’s Law (I)
Induced emf is proportional to the rate of change of magnetic flux FB passing through a loop of area A
FB = BAcosq
q is angle between B and a line perpendicular to the face of the loop
Flux applet
Courtesy Dept. of EE Surrey University

5. Nature of Magnetic Flux
FB = BAcosq is a scalar
Above formula comes from “dot product” of B and A whereas
F =Bqvsinq comes from “cross” or vector product B x v
Unit of magnetic flux is tesla-meter2 or weber

6. Ways of Changing Flux Move coil into or out of field
Change area of coil
Rotate coil so number of field lines changes
Change field strength
Ways Flux will not change
Rotate coil around field line – doesn’t change number of field lines
Slide coil at constant angle within field

7. Faraday’s Law (II) Emf = -N D FB/ Dt
Magnetic flux is also proportional to total number of field lines passing through loop
When q = 00 magnetic flux FB = BA (A is area of loop perpendicular to magnetic field)
When q = magnetic flux is zero; no field lines pass through loop. Mathematically
Emf = -N D FB/ Dt
N is number of loops

8. Almost calculus
D FB/ Dt is time rate of change of flux

9. Simple example
A square loop of side a enters a region of uniform magnetic field B in time Dt = one second. Write an expression for the voltage induced during that interval
Emf =-N D FB/ Dt = -a2B/1 second =-a2B

10. Current direction?
How do we know in what direction, clockwise or counterclockwise the induced current will flow?
Energy conservation plays a role
Energy in the current and voltage must come from somewhere
How this works is called Lenz’s Law

11. Lenz’s Law
Minus sign in Faraday’s Law reminds us that
Induced current produces its own magnetic field
This field interacts with original field to make a force
Work must be done against this force to produce induced current or conservation of energy will be violated
An induced emf always gives rise to a current whose magnetic field opposes the original change in flux Applet

12. How Current Varies
Link (demonstrates Lenz’s Law with bar magnet and loop)

13. In Other Words
Physical motion that induces current must be resisted by magnetic forces
Something has to do work to induce the current, otherwise energy conservation is violated

14. What is Direction of Current?
loop
Current clockwise
Field in this region toward us

15. What is Direction of Current?
loop
Field in this region away from us
Current counter clockwise

16. Changing Area – What is the direction of induced current?
Field away from us xxx
Field toward us
Answer to CW. Induced field away to restore existing field
Answer to 2. CCW. Field toward us to restore existing field
Loop area shrinks

17. What if Loop Area Increases?
Answers reverse
1 CCW
2 CW

18. Another Example of Lenz’s Law
When field is increasing, induced field opposes it
When field is decreasing, induced field acts in the same direction
Diagram courtesy Hyperphysics web site

19. Example: Square coil side 5. 0 cm with 100 loops removed from 0
Example: Square coil side 5.0 cm with 100 loops removed from 0.60T uniform field in 0.10 sec. Find emf induced.
Find how flux FB = BA changes during Dt = 0.10 sec.
A =
Initial FB
Final FB = zero
Change in flux is
Emf = -(100)(-1.5 x 10-3 Wb)/(0.10 s) =
2.5 x 10–3 m2
1.5 x 10-3 Wb
-1.5 x 10-3 Wb
1.5 volts

20. Example, continued
If resistance of coil is 100 ohms what are current, energy dissipated, and average force required?
I = emf/R = 1.5v/100 ohms =
E = Pt = I2Rt=
F = work required to pull coil out/distance = energy dissipated in coil/distance = W/d =
15mA
2.25 x 10-3 J
0.050 N
Use d = 0.05 m since no flux change until one edge leaves field

21. EMF in a Moving Conductor
Courtesy P Rubin, university of Richmond

22. Moving Rod Changes Area of Loop
Let rod move to right at speed v
Travels distance Dx = v Dt
Area increases by DA = LDx=L v Dt
By Faraday’s law
Emf = D FB/ Dt = BDA/Dt = BLvDt/Dt = BLv
B, L and v must be mutually perpendicular

23. Alternate Derivation of emf = BLv
Force on electron in rod moving perpendicular to magnetic field strength B with speed v is F=qvB acting downward
Produces emf with top of rod +
CCW conventional current as rod slides to right
Work to move a charge through rod against potential difference is
W = Fd = qvBL. Emf is work per unit charge BLv

24. Blv Example: Voltage across an airplane wing
Airplane with 70 m wing travels 1000 km/hr through earth’s field of 5 x 10-5 T. Find potential difference across wing. Is this dangerous?
Emf = Blv =
Could such a potential difference be used to reduce the aircraft’s need for fuel?
(5.0 x 10-5 T) (70m) (280 m/s) = 1.0volt

25. The Generator
Generators and alternators work by rotating a coil in a magnetic field. They produce alternating current.