Electromagnetic Induction

1
Electromagnetic Induction

• Electricity from Magnetism

2
Induced Current

• When a conductor is moved in a magnetic field,
  current can be induced (caused)
• Faradays 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
Faradays 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 doesnt change
  number of field lines
• Slide coil at constant angle within field

7
Faradays Law (II)

• 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 900 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 Lenzs Law

11
Lenzs Law

• Minus sign in Faradays 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 Lenzs 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?

1. Field away from us xxx
2. Field toward us . . .

Answer to 1. 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 Lenzs 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 0.60T 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 103 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 LDxL v Dt
• By Faradays 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 FqvB
  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 earths 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 aircrafts 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.