• Electromagnetic induction is when an e.m.f is induced in a closed circuit conductor due to it moving through a magnetic field
• This happens when a conductor cuts through magnetic field lines
• The amount of e.m.f induced is determined by the magnetic flux
  • This is the total magnetic field that passes through a given area
  • It is a maximum when the magnetic field lines are perpendicular to the area
  • It is at a minimum when the magnetic field lines are parallel to the area
• The magnetic flux is defined as:

The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

• In other words, magnetic flux is the number of magnetic field lines through a given area

• Magnetic flux is defined by the symbol Φ (greek letter ‘phi’)
• It is measured in units of Webers (Wb)
• Magnetic flux can be calculated using the equation:

Φ = BA

• Where:
  • Φ = magnetic flux (Wb)
  • B = magnetic flux density (T)
  • A = cross-sectional area (m²)

• When the magnet field lines are not completely perpendicular to the area A, then the component of magnetic flux density B perpendicular to the area is taken
• The equation then becomes:

Φ = BA cos(θ)

• Where:
  • θ = angle between magnetic field lines and the line perpendicular to the plane of the area (often called the normal line) (degrees)

• This means the magnetic flux is:
  • Maximum = BA when cos(θ) =1 therefore θ = 0^o. The magnetic field lines are perpendicular to the plane of the area
  • Minimum = 0 when cos(θ) = 0 therefore θ = 90^o. The magnetic fields lines are parallel to the plane of the area
• An e.m.f is induced in a circuit when the magnetic flux linkage changes with respect to time
• This means an e.m.f is induced when there is:
  • A changing magnetic flux density B
  • A changing cross-sectional area A
  • A change in angle θ

Worked example

Part (a)

Step 1:            Write out the known quantities

Cross-sectional area, A = 40 cm × 73 cm = (40 × 10^-2) × (73 × 10^-2) = 0.292 m²

Magnetic flux density, B = 1.8 × 10^-5 T

Step 2:             Write down the equation for magnetic flux

Φ = BA

Step 3:            Substitute in values

Φ = (1.8 × 10^-5) × 0.292 = 5.256 × 10^-6 = 5.3 × 10^-6 Wb

Part (b)

The magnetic flux will be at a minimum when the window is opened by 90^o and a  maximum when fully closed or opened to 180^o