Inducing EMF

• EM induction is an action-at-a-distance phenomenon
• EMF is induced when magnetic flux linking a conductor changes either by:
  • the change in the number of lines linking B-field
  • the change in the number of field lines being cut
• For example, moving the coil from A to B below:
  
  • the number of lines linked increases from 3 to 5
  • the number of lines cut increases from 0 to 2
  • Hence, and EMF is induced

Magnetic Flux Linkage

• Magnetic Flux is the product of magnetic flux density and the area normal to the field through which the field is passing
  • Φ = BA
• 1 Weber (Wb) is the flux that passes through an area of 1 m² when the  magnetic flux density is 1 Tesla
  • 1 Wb = 1 Tm²
• Magnetic Flux Linkage is the product of magnetic flux and the number of turns
  • Magnetic flux linkage = NΦ
• Factors affecting magnitude of induced EMF:
  • Magnetic field density, B
  • Speed of motion of the magnet, v
  • Number of turns of the coil, N

Faraday’s and Lenz’s Law

• Faraday’s Law states that the magnitude of the induced EMF is proportional to the rate of change of magnetic flux-linkage
  • V = ^dNΦ/_dt
• Lenz’s Law states that the direction of the induced EMF is such that it tends to oppose the flux change causing it
  • V = ^dNΦ/_dt
    

Examples

1. Use Faraday’s law to explain why
   1. there is a reading on the voltmeter
      • Moving the magnet causes a change in the flux linkage
   2. this reading varies in magnitude
      • The speed of the magnet varies, so varying the rate of change of flux
   3. the reading has both positive and negative values
      • The magnet changes direction of motion
2. A small rectangle coil ABCD contains 140 turns of wire
   The coil is held between the poles of a large magnet so that the coil can rotate about an axis through its center. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 × 10^-3 Nm.
   1. What position to the magnetic field should the coil be in for maximum torque
      • The maximum torque is achieved when the system is parallel to the plane. When it is normal to the plane, there is no perpendicular distance between the two forces, therefore, minimum or zero torque
   2. For the coil in the position shown above, calculate the magnitude of the force on side AB
      • Torque = Force × perpendicular distance between forces
      • 2.1 × 10^-3 = 2.8 × 10^-2 × f
      • f = 0.075 N
   3. Show that the magnetic flux density, B, is 70 mT
      • F = BIl
      • Using the force calculated above:
        • 0.07 = B × 170 × 10^-3 × 4.5 × 10^-2
        • B = 9.80 T
      • The value calculated is for 140 turns, divide by 140 to get that of 1 turn:
        • ^9.8/₁₄₀ = 0.07 T = 70 mT
   4. The current in the coil is switched off and the coil is turned through an angle of 90° in a time of 0.14 s. Calculate the average EMF induced
      • Firstly, calculate Φ from B calculated above:
        • Φ = BA
        • Φ = 70 × 10^-3 × 2.8 × 10^-2 × 4.5 × 10^-2
        • Φ = 8.82 × 10^-5 Wb
      • Using Faraday’s Law:
        • V = ^dNΦ/_dt
        • V = ^{140 × 8.82 × 10-5}/_0.14
        • V = 0.0882 v