Magnetic Flux & Faraday’s Law

You’ll be able to

Define magnetic flux and identify the three ways to change it
Use Faraday’s law to calculate the magnitude of an induced EMF
Recognize that only a changing flux induces an EMF

Magnetic flux: field through a loop

Magnetic flux (Φ) measures how much magnetic field passes through a loop of area A: Φ = BA cosθ, where θ is the angle between the field and the normal (perpendicular) to the loop. Flux is largest when the field points straight through the loop (θ = 0°) and zero when the field lies in the plane of the loop (θ = 90°). Its unit is the weber (Wb = T·m²). Flux is the key quantity because changing it is what generates electricity.

Faraday’s law: a changing flux drives a current

Faraday’s law is the heart of electric generators: a changing magnetic flux through a loop induces a voltage (EMF) around it. The faster the flux changes, the bigger the induced EMF — and adding N turns of wire multiplies it N times. There are exactly three ways to change the flux Φ = BA cosθ: change the field strength B, change the loop’s area A, or change the orientation θ (rotate the loop). A steady flux, no matter how strong, induces nothing. Motion or change is essential.

Magnetic flux and Faraday’s law

Φ = B · A · cosθ · |EMF| = N · |ΔΦ / Δt|

ΔΦ/Δt is the rate of change of flux. N is the number of turns in the coil. The induced EMF depends on how fast the flux changes, not on the flux itself.

Worked example

A single circular loop of area 0.20 m² lies perpendicular to a magnetic field. The field increases steadily from 0.50 T to 1.5 T in 2.0 s. Find the magnitude of the induced EMF.

1.The loop is perpendicular to the field, so θ = 0° and Φ = BA.
2.Change in flux: ΔΦ = (ΔB)(A) = (1.5 − 0.50)(0.20) = (1.0)(0.20) = 0.20 Wb.
3.Apply Faraday’s law with N = 1: |EMF| = ΔΦ/Δt = 0.20 / 2.0.
4.Compute: 0.20 / 2.0 = 0.10 V.

Answer: 0.10 V is induced around the loop while the field is changing.

Checkpoint

A single loop of area 0.20 m² sits perpendicular to a magnetic field that increases from 0.50 T to 1.5 T in 2.0 s. What is the magnitude of the induced EMF?

Tip

Whenever you see “induced EMF,” hunt for what is changing: is the field growing, the loop rotating, or its area shrinking? If nothing about Φ = BA cosθ is changing over time, the induced EMF is zero.

Checkpoint

Which situation induces NO EMF in a stationary conducting loop?

On the exam

Faraday’s law depends on the rate of flux change, not the flux itself. A huge steady field induces nothing; a small field that changes quickly can induce a large EMF. Always compute ΔΦ/Δt, and multiply by N for a coil.

Answer the 2 checkpoints as you read.