Magnetic Flux

Imagine holding a wire loop near a bar magnet. The more the magnetic field lines that "pierce" through the loop, the stronger the effect on any current induced in it. The quantity that measures this "piercing" is called magnetic flux.

Think of it like sunlight falling on a solar panel:

• Panel facing the sun directly → maximum light captured (maximum flux)
• Panel tilted at an angle → less light captured (reduced flux)
• Panel edge-on to the sun → zero light captured (zero flux)

Magnetic flux is the equivalent measure of magnetic field lines passing through a surface.

The magnetic flux linked with any surface is equal to the total number of magnetic lines of force passing normally through it.

Or

Magnetic Flux (Φ_B​) is defined as the total number of magnetic field lines passing normally through a given surface area placed in a magnetic field.

\[\Phi_B=\vec{B}\cdot\vec{A}=BA\cos\theta\]

For a non-uniform field or a curved surface, flux is calculated by summing contributions over infinitesimally small area elements \[d\vec{A}\]:

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

For a coil of N turns, each contributing equally:

Φ = N B A cos θ (flux linkage)

SI Unit

Weber (Wb): 1Wb = 1T ⋅ m² = 1 V ⋅ s

Also expressed as: Wb = Ω ⋅ C = H ⋅ A

CGS Unit

Maxwell (Mx): 1Wb = 10⁸ Mx ⟺ 1 Mx = 10⁻⁸ Wb

Dimensional Formula

Magnetic flux increases when:

• B increases → stronger magnetic field → more field lines per unit area
• A increases → larger surface area → more field lines pass through
• θ decreases (toward 0°) → surface becomes more perpendicular to B → more lines cross it

Flux changes occur when any one or more of B, A, or θ changes with time, and it is this change in flux that drives electromagnetic induction.

• Magnetic flux is a scalar quantity (result of dot product of two vectors)

• It can be positive, negative, or zero depending on orientation

• For a closed surface, the net magnetic flux is always zero because magnetic monopoles do not exist and field lines always form closed loops:
  \[\oint\vec B\cdot d\vec A\] = 0

This is Gauss's Law for Magnetism.

Magnetic flux is the foundation of Faraday's Law of Electromagnetic Induction: