20.5 Electromagnetic Induction

1. Magnetic Flux

What is Magnetic Flux?

Imagine a magnetic field made up of invisible lines flowing through space — we call these magnetic field lines. Now imagine holding a flat loop of wire in that field. Some of those field lines will pass through the area of the loop.

Magnetic flux (symbol: Φ, the Greek letter "phi") is a measure of how many magnetic field lines pass through a given area. More precisely:

• Magnetic flux density (symbol: B, unit: Tesla, T) is the strength of the magnetic field — how tightly packed the field lines are.
• Cross-sectional area (symbol: A, unit: m²) is the area of the surface the field lines are passing through.
• Magnetic flux (symbol: Φ, unit: Weber, Wb) is the total "amount" of field passing through that area.

The Formula

$\Phi = BA$

Maximum and Minimum Flux

The amount of flux through an area depends on the angle between the field lines and the surface:

• Maximum flux: when the field lines are perpendicular to the plane of the area (i.e., they pass straight through it at 90°). In this case, Φ = BA.
• Minimum flux (zero): when the field lines are parallel to the plane of the area (i.e., they skim along the surface and don't pass through it at all). In this case, Φ = 0.

Think of it like rain falling on an umbrella. If you hold the umbrella flat (horizontal), all the rain hits it — maximum. If you tilt it completely sideways (vertical), no rain hits it — zero.

When the Field is at an Angle

If the magnetic field lines are not perfectly perpendicular to the area, you must take the component of B that is perpendicular. The formula becomes:

$\Phi = BA\cos\theta$

where θ is the angle between the magnetic field lines and the normal to the area (the normal is an imaginary line drawn at right angles to the surface).

• When θ = 0°: cos 0° = 1, so Φ = BA (maximum — field is perpendicular to plane)
• When θ = 90°: cos 90° = 0, so Φ = 0 (minimum — field is parallel to plane)