Magnetic flux measures how much magnetic field passes through a specified area. For a uniform magnetic field crossing a flat surface, calculate it using , where is the angle between the magnetic field and the normal to the surface.
This is Additional higher level (AHL) content in topic D.4 Induction and is assessed only in IB Physics HL.
In IB Physics D.4 Induction, magnetic flux is defined by
where:
The cosine factor selects the component of the magnetic field perpendicular to the surface: . Therefore, .
Equivalently, you can treat as the projected area perpendicular to the field. Rotating the loop changes this projected area, so the flux changes even if both and remain constant.
| Field orientation | Angle | Magnetic flux |
|---|---|---|
| Perpendicular to the surface | Maximum: | |
| At an intermediate angle | Between and | |
| Parallel to the surface | Zero |
For example, a field passes through a loop at to its normal:
If the same loop is turned so its normal is parallel to the field, and the flux becomes . Turning it through makes the field parallel to the surface and reduces the flux to zero.
A common misconception is measuring from the plane of the surface. It must be measured from the normal. For a coil of turns, is the magnetic flux linkage, not the flux through one turn.
HL questions may ask you to calculate flux or apply Faraday's law, . State the angle reference, convert area into , and distinguish clearly between and . In calculations, keep the cosine value unrounded until the final numerical answer is obtained.
