Magnetic Induction

1
Magnetic Induction

• Review of Chapter 22

2
Induced EMF (motional EMF)

• Potential difference (voltage) created by a
  changing magnetic field that causes current to
  flow through a wire.
• e v B L where e is the electromotive force, v
  is the relative velocity between the charged
  object and the field, B is the magnetic field
  strength and L is the length of the object (or
  wire) passing through the field.
• perpendicular The equation above assumes that v,
  B, and L are mutually

3
Magnetic Flux

• Definition the number of field lines that pass
  through an area.
• FB BA cos Q where FB is the magnetic flux, B is
  the magnetic field, A is the area of the region
  that the flux is passing through and Q is the
  angle between B and A
• e DF/Dt this equation for a single conductor
  is the basis for Faradays Law

4
Faradays Law

• Definition describes exactly how much EMF is
  induced by a changing magnetic flux.
• Equation e -N DF
• Dt
  

5
Lenzs Law

• Lenzs law describes the direction of the induced
  current.
• Lenz stated that the direction of the induced
  current always opposes the increase in flux.
• In other words, the induced current will create a
  magnetic field opposite to the existing magnetic
  field causing the current.

6
Practice Problem

• A circular loop of wire of negligible resistance
  and a radius of 20 cm is attached to the circuit
  shown. Each resistor has a value of 10 W. The
  magnetic field of the Earth point up as shown and
  has a value of 5 x 10-5 T. The circular loop
  rotates about a horizontal axis that passes
  through the center of the loop at a rate of 500
  rev/s and remains connected to the circuit the
  entire time

7
Practice Problem (Continued)

• Determine the magnetic flux through the loop when
  in the orientation shown in the picture.
• Determing the maximum magnetic flux through the
  loop.
• Estimate the average value of the induced EMF in
  the loop.
• Estimate the average current in resistor C

8
Q1 - Magnetic Flux as shown

• The flux equals zero because the field points
  along the loop, never going through the loop.

9
Q2 - Maximum Flux

• Flux is at a maximum when the loop is
  perpendicular to the page. The flux will then be
  equal to BA.
• B 5 x 10-5 T
• A pr2 p (.20)2 .126
• F 6.3 x 10-6 Tm2

10
Q3 - Average EMF for the Loop

• e DF/Dt, and it takes 1/4 turn to go from the
  minimum to maximum flux. Since it takes 1/500 of
  a second to make 1 turn, it only takes 1/2000 of
  a second to reach the first maximum. Using the
  equation above, the EMF is 6.3 x 10-6 Tm2 /0.0005
  s .013 V

11
Q4 - Current in Resistor C

• The circuit can now be treated as if there were a
  13 mV battery attached to it.
• Re of resistors B and C is 5? and RT is 15?.
• IT 8.4 x 10-4 A
• Since B and C are equal, the current is split
  equally among them and is 4.2x10-4 A.