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 given area. Here, the area is the space under influence of magnetic field lines.

The current flows in an electric circuit. In a 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 are magnetic lines of forces. The magnetic lines of forces is ;

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** – 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 field and normal to the surface is is 90 ^{°} , B is parallel to the surface and,

If θ is 0^{°}, Cos 0 = 1, When the angle between 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 produce an electromotive force. The below given formula shows 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 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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