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Magnetic Flux (CIE A Level Physics)

Revision Note

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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

Magnetic flux diagram, downloadable AS & A Level Physics revision notes

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:

capital phi space equals space B A

  • 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:

capital phi space equals space B A cos open parentheses theta close parentheses

  • 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

Flux perpendicular and at an angle, downloadable AS & A Level Physics revision notes

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 = 0o. The magnetic field lines are perpendicular to the plane of the area
    • minimum = 0 when cos(θ) = 0 therefore θ = 90o. 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 length of 73 cm as shown in the figure belowWE Calculating Magnetic Flux question image, downloadable AS & A Level Physics revision notesThe 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

a) Calculate the magnetic flux through the window when it is closed

b) Sketch the graph of the magnetic flux against angle between the field lines and the normal when the window is opened and rotated by 180°

Answer:

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

capital phi space equals space B A

Step 3: Substitute in values

capital phi space equals space open parentheses 1.8 space cross times space 10 to the power of negative 5 end exponent close parentheses space cross times space 0.292 space equals space 5.256 space cross times space 10 to the power of negative 6 end exponent space equals space 5.3 space cross times space 10 to the power of negative 6 end exponent space Wb

Part (b)

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

WE Calculating Magnetic Flux graph solution, downloadable AS & A Level Physics revision notes

Examiner Tip

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

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.