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.

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 Ø_{m}.

## 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;

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

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,

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 through a closed surface**

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

**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.

Where* ε– *electromotive force

**v**– velocity of the boundary

**E**– electric field

**B**– magnetic field

**ø**

_{B – }magnetic flux through the open surface

**d**– infinitesimal vector element of the contour of ∂Σ

**ℓ**## **Properties of Magnetic Flux**

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

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