Electromagnetism

• Magnetic flux


  A measure of the amount of magnetic field passing through an area
• Magnetic flux has units of weber (Wb), which is T m²
• Magnetic flux

  • Depends on the angle, θ, between the normal to the area
  • Maximum when field is perpendicular to area (θ = 0°)
  • Zero when field is parallel to area (θ = 90°)
• Magnetic flux can change if the field, area, or angle between them changes
• Changing magnetic flux


  1. Changing field

  2. Changing area

  3. Changing angle between field and area
• Flux is a scalar quantity, not a vector
• Rate of change of flux

  • Constant if flux changes linearly with time
  • Varies if flux changes non-linearly with time
• An induced emf is created by a changing magnetic flux
• Faraday's Law


  ε = -Δ(Φ)/Δt
• Faraday's Law: Induced emf is proportional to the rate of change of magnetic flux
• Ways to induce an emf


  • Change the magnetic field
  • Change the area
  • Change the angle between field and area
• Emf


  Energy per unit charge, not a force. An emf provides the energy to make a current flow.
• Electromagnetic induction


  1. Changing magnetic flux through an area induces an electric field

  2. Induced electric field produces an induced emf

  3. Induced emf is created by a changing magnetic flux

  4. Placing a loop of wire in a magnetic field and changing the flux through the loop induces an emf
• Faraday's Law


  The magnitude of the induced emf caused by a changing magnetic flux
• Faraday's Law units are Tm2 s-1, which is the same as volts, V
• Inducing an emf


  • Change the magnetic field, B
  • Change the area, A
  • Change the angle, θ, between the area and the field
• Coils with multiple loops can induce a larger emf by adding the emf in all loops
• Emf vs Potential Difference

  Emf is the energy per unit charge available to a charged particle, potential difference is the unique difference in potential energy per unit charge between two points in an electric field
• Potential difference is a type of emf, but not all emfs are potential differences
• Lenz's Law: An induced emf acts to produce an induced current in the direction that causes a magnetic flux that opposes the change in flux that induced the emf
• Eddy currents


  Induced currents that form loops and spirals in a conductive material when exposed to a changing magnetic field
• Electromagnetic induction


  A changing magnetic flux through a region induces an emf (electromotive force)
• Emf


  The energy available per unit charge. An induced emf can create an induced current if there are free charge carriers and a path for them to flow along
• Faraday's Law


  The induced emf created by a changing magnetic flux is given by: ε = -N Δ Φ / Δ t
• The flux can change if the magnetic field, area or angle between the area and the field changes
• Lenz's Law


  The induced emf is such that it opposes the change in flux that created it
• An induced current creates a magnetic field that acts to oppose the change in flux
• Eddy currents


  1. Induced currents in any material with free charge carriers

  2. Electrons move in circles, forming loops and spirals of current

  3. Eddy currents create magnetic fields that oppose the changing flux from the moving magnet

  4. Eddy currents result in heating of the material due to resistance
• A changing magnetic flux through a region induces an emf
• An emf is the energy available per unit charge. An induced emf can create an induced current if there are free charge carriers and a path for them to flow along
• Lenz's Law states that the induced emf is such that it opposes the change in flux that created it
• Transformer


  Consists of two solenoids, or coils, of wire placed near each other so that an alternating current (AC) in the primary coil can induce a current in the secondary coil

  
• AC current varies sinusoidally with time
• Amplitude


  The maximum current, Imax, sometimes also called the peak current Ipeak
• Peak-to-peak current


  The difference between the maximum and minimum currents, Ipeak–peak
• Period


  The time it takes for the current to go from its maximum value through a complete cycle and back to its maximum again, T
• Frequency


  The number of cycles per second, f = 1/T
• Root mean square (rms) value


  The single value of emf that would deliver the same power as the original AC emf: Vrms = Vpeak/√2
• Flux linkage


  How much flux from one coil passes through the other coil in a transformer
• The alternating current in the primary coil creates a sinusoidally time-varying magnetic field, which magnetises the whole core of the transformer