Magnetic Flux (Cambridge International A-Level Physics)

Magnetic Flux Definition

• Electromagnetic induction is the process of inducing an e.m.f in a conductor when there is relative movement between a charge and a magnetic field

  • This can be observed using a magnet and a coil or a solenoid

• This happens when a conductor cuts through magnetic field lines

• The amount of e.m.f induced is determined by the magnetic flux

• The amount of magnetic flux varies as the coil rotates within the field

  • The flux is the total magnetic field that passes through a given area
  • It is a maximum when the magnetic field lines are perpendicular to the plane of the area
  • It is 0 when the magnetic field lines are parallel to the plane of 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 a measure of the number of magnetic field lines passing through a given area

Maximum and minimum magnetic flux

The magnetic flux is maximum when the magnetic field lines and the area they are travelling through are perpendicular

Calculating Magnetic Flux

• 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:

$\\Phi = B A \cos ( \\theta )$

• Where:

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

Increasing and decreasing magnetic flux

The magnetic flux increases as the angle between the field lines and normal decreases

• 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 An aluminium window frame has a width of 40 cm and a length of 73 cm, as shown in the figure below

The frame is hinged along the vertical edge AC. When the window is closed, the frame is normal to the Earth’s magnetic field with magnetic flux density 1.8 × 10^-5 T.

Calculate the magnetic flux through the window when it is closed.

Answer:

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

$\\Phi = ( 1.8 \times 10^{- 5} ) \times 0.292 = 5.256 \times 10^{- 6} = 5.3 \times 10^{- 6} \text{Wb}$

Exam Hint Consider carefully the value of θ, which is the angle between the field lines and the line normal (perpendicular) to the plane of the area through which the field lines pass. If it helps, drawing the normal on the area provided will help visualise the correct angle.