Electromagnetism: (a) magnetic flux Φ; the unit weber; Φ = BA cos θ

The idea

Magnetic flux Φ measures the amount of magnetic field passing through a surface. For a uniform field B through area A, Φ = BA cos θ, where θ is the angle between the field direction and the normal to the surface. The unit of flux is the weber, Wb, and 1 Wb = 1 T m². When the field is perpendicular to the surface, θ = 0° and Φ = BA; when the field is parallel to the surface, θ = 90° and Φ = 0. Example: a coil of area 2.0 × 10⁻³ m² in a field of 0.50 T with its normal at 60° to the field has Φ = 0.50 × 2.0 × 10⁻³ × cos 60° = 5.0 × 10⁻⁴ Wb.

What earns the marks

• Defines magnetic flux as the product of flux density and the area perpendicular to the field.
• Uses Φ = BA cos θ with θ measured between the field direction and the normal to the surface.
• States that the unit of magnetic flux is the weber, where 1 Wb = 1 T m².
• Applies the equation to calculate flux for a given field, area and orientation.

Common mistakes and how to put them right

• Measuring θ between the field and the surface rather than between the field and the normal.

  Put it right: θ is the angle between B and the normal to the area.

• Forgetting the cos θ factor when the surface is tilted.

  Put it right: Only the component of B perpendicular to the area contributes to the flux.

• Using the wrong unit for flux.

  Put it right: Flux is measured in weber, Wb, equivalent to T m².

Exam tips

• Identify the normal to the surface first, then measure θ from the field direction to that normal.
• Check the orientation: θ = 0° gives maximum flux BA, and θ = 90° gives zero flux.
• Convert area to m² and flux density to T before calculating flux in Wb.