RP11 - Magnetic Flux Linkage

• What pieces of apparatus can be used to measure the induced emf inside a current carrying circular coil?

  A search coil connected to an oscilloscope
• Why must an alternating current source be used in this experiment?

  An AC source should be used so that the magnetic flux through the search coil is constantly changing
• How can an oscilloscope be used to measure the induced EMF?

  • When connected to the search coil, the oscilloscope will show the waveform of the induced EMF
  • By turning the time base off, this will become a vertical line that gives the peak to peak value of the EMF
• What preliminary experiment will need to be undertaken before carrying this experiment out?

  • A preliminary experiment will be needed to determine a suitable voltage and frequency for the circular coil
  • The induced emf must be large enough to be easily measured using the search coil and oscilloscope
• What is magnetic flux?

  • Magnetic flux is equal to the product of the magnetic flux density and the area through which it passes
  • It can be thought of as the number of field lines passing through a given area
• Suggest how angle measurements could be taken in this experiment

  • A circular protractor card could be positioned under the circular coil and fixed in place with an optical pin
  • This allows the angle between the circular coil and the search coil to be measured from the same position each time
• In what orientation will the maximum induced EMF and flux linkage occur in the search coil?

  • The maximum induced emf and flux linkage will occur when the search coil is perpendicular to the magnetic field lines
  • This is when the angle is equal to 0 degrees
• Why might an ammeter be required when carrying out the preliminary experiment?

  • It is important to ensure that the current passing through the coil doesn't exceed the manufacturer's guidelines
• In which orientation should the induced EMF be at a minimum?

  • The induced EMF should be zero when the search coil is parallel to the magnetic field lines
  • This is when the angle is equal to 90 degrees
• What is magnetic flux linkage?

  Magnetic flux linkage is equal to the magnetic flux passing through a coil multiplied by the number of turns that cut this flux
• What is the unit of magnetic flux?

  Webers (Wb)
• Gradient Derivation:

  N = BANcos (x)

  I = I_0cos(ωt) + B = B_0cos(ωt)

  N = BANcos(x) = B_0cos(ωt)ANcos(x)

  E = ΔN /Δt = - B_0ANΔsin(ωt)cos(x)

  E_0 = B_0ANω cos(x) when sin (ωt) = 1 or -1

  Where:

  E_0 = y

  B_0ANω = x

  cos(x) = m