Skip to content

Magnetic Flux

Source lecture(s): SC134 Lec11

Intuition

Flux measures how many magnetic field lines pass through a loop—it is the bridge between \(B\) and induced EMF.

Formal Definition

\[\Phi_B = \int \vec{B}\cdot d\vec{A}\]

Mathematical Formulation

Uniform \(B\) through flat loop: \(\Phi_B = BA\cos\theta\) Unit: 1 weber (Wb) = 1 T·m\(^2\).

Derivation

Surface integral of normal component; analogous to electric flux but with \(B\).

Worked Example

Loop area \(0.1\,\text{m}^2\) at \(30^\circ\) to 0.5 T field: \(\Phi = 0.5\times0.1\times\cos30^\circ \approx 0.043\,\text{Wb}\).

Common Mistakes

  • Using open surface instead of any surface bounded by loop.
  • Forgetting \(\cos\theta\).

Quiz

Q1. Can flux change if \(B\) is constant?

Answer

Yes—if the loop rotates or changes area.