What is Magnetic Flux? Definition & Properties

The number of magnetic field lines passing through a closed area is called magnetic flux. In other words, it is the total magnetic field in a given area. Here, the area is the space under influence of magnetic field lines.

Magnetic Flux lines

The current flow in an electric circuit. In the same way, the flux flows in a magnetic circuit. Flux is thus analogous to electric current. The Greek letter Phi or Phi suffix B is its symbol. Its symbol is Ø and  Øm.

Magnetic Flux Formula

Now let us derive its formula for better understanding.

The number of field lines passing through a given area is magnetic lines of forces. The magnetic lines of forces are;

magnetic flux formula

The magnetic flux also depends on the angle between the magnetic field lines surface area.

magnetic flux formula considering the angle between B

where
B – Magnitude of the magnetic field
S – Surface area
θ – the angle between the magnetic field lines and perpendicular distance normal to the surface area

If θ is 90°, Cos θ = 0, When the angle between the field and normal to the surface is 90 °, B is parallel to the surface and,

magnetic flux when angle is 90 degree

If θ is 0°, Cos 0 = 1, When the angle between the field and normal to the surface is is 0 °, B is perpendicular to the surface and,

magnetic flux when angle is 0 degree

Magnetic flux through a closed surface

According to Gauss’s law, the total magnetic flux through a closed surface is equal to zero.

flux in closed area

Magnetic flux for open surface

Current in the looped conductive wire cause change in the flux. And, this changed flux produces an electromotive force. The below-given formula shows the relationship between generated EMF with change in the flux.

changing magnetic flux in a wire

Where
ε– electromotive force
v – velocity of the boundary
E – electric field
B – magnetic field
øB –  magnetic flux through the open surface
dℓ – infinitesimal vector element of the contour of ∂Σ

Properties of Magnetic Flux

  1. The magnetic lines form a closed loop.
  2. The lines start from the north pole and ends in the south pole.
  3. Magnetic lines lines never intersect each other.
  4. Magnetic lines of forces that are parallel, and in the same direction repel each other.
  5. The lines of force are like a stretched elastic cord.

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