Skip to content
Stan’s Legacy
Sign in

Magnetic flux through a coil

How much magnetic flux links a coil sitting in a field of a given strength, area and angle?

The formula
Φ=B⁢A⁢cosθ
Φ
Magnetic flux, Wb
B
Field strength, T
A
Area, m²
θ
Angle from the normal, °
LaTeX 
Φ = B \cdot A \cdot \cos(θ)

Work it out

G

The magnetic flux density at the coil. Core datasheets of the period are quoted in gauss.

cm²

The cross-sectional area the field passes through.

°

The angle between the field and the coil's normal. Zero is face-on, where linkage is greatest.

or see a worked example with typical numbers

Method

  1. Convert the field to tesla and the area to square metres. Flux is a product of the two in SI, and gauss and square centimetres are both a hundred-to-one from that.
  2. Convert the angle from degrees to radians.
  3. Multiply the field by the area and by the cosine of the angle. Face-on (0°) gives the full product; edge-on (90°) gives zero, however strong the field is.

Assumptions

  • The field is uniform across the coil's area. A real EPG field is not, especially near a pole face; this treats the coil as small enough, or the field as even enough, that one number describes it.
  • The coil is a flat loop (or a stack of identical turns, each contributing the same flux) rather than a wound solenoid threading its own field.
  • No fringing or leakage is modelled. A real magnetic circuit loses some flux around the edges of the gap; this is the ideal figure.