Magnetic flux measures how much magnetic field passes through a surface, such as the area inside a wire loop. It matters because it connects the geometry of a loop to the strength and direction of a magnetic field. A loop facing directly into a magnetic field has maximum flux, while a loop turned edge-on has zero flux.
This idea is central to generators, transformers, motors, and many sensors.
Key Facts
- Magnetic flux is ΦB = B A cos θ for a uniform magnetic field through a flat surface.
- ΦB is magnetic flux, B is magnetic field strength, A is area, and θ is the angle between B and the area vector.
- The SI unit of magnetic flux is the weber, where 1 Wb = 1 T m^2.
- Flux is maximum when θ = 0°, so ΦB = B A.
- Flux is zero when θ = 90°, so ΦB = 0 because the field is parallel to the surface.
- Changing magnetic flux induces an emf: ε = -N ΔΦB / Δt.
Vocabulary
- Magnetic flux
- Magnetic flux is the amount of magnetic field passing through a chosen surface.
- Area vector
- The area vector is a vector perpendicular to a surface with magnitude equal to the surface area.
- Weber
- The weber is the SI unit of magnetic flux and equals one tesla square meter.
- Electromagnetic induction
- Electromagnetic induction is the production of an emf when magnetic flux through a circuit changes.
- Faraday's law
- Faraday's law states that the induced emf depends on the rate of change of magnetic flux through a circuit.
Common Mistakes to Avoid
- Using the angle between the magnetic field and the loop surface is wrong because ΦB = B A cos θ uses the angle between the magnetic field and the area vector, which is perpendicular to the surface.
- Forgetting the cosine factor is wrong because flux depends on orientation, not just field strength and area.
- Treating flux as the same as magnetic field is wrong because magnetic field is measured in tesla while flux is measured in webers and includes area and angle.
- Ignoring the number of turns in a coil is wrong because the induced emf depends on the total flux linkage, so ε = -N ΔΦB / Δt for N identical turns.
Practice Questions
- 1 A circular loop has area 0.050 m^2 and is in a uniform magnetic field of 0.80 T. The area vector makes a 30° angle with the field. Calculate the magnetic flux through the loop.
- 2 A 25-turn coil experiences a flux change from 0.012 Wb to 0.004 Wb per turn in 0.20 s. What is the magnitude of the induced emf?
- 3 A conducting loop is rotated from face-on to edge-on in a steady magnetic field. Explain how the magnetic flux changes and why an emf is induced during the rotation.