# property>magnetic flux

## What is Magnetic Flux?

The product of a magnetic field passing through a surface placed perpendicular to the field is known as magnetic flux. More generally it is the scalar product of the magnetic field and the area vector.

The magnetic flux through a surface is directly proportional to the net density or number of magnetic field lines passing through that surface. The magnetic flux is defined by the integral of the magnetic field over the area of the surface. Where the surface S is a planar surface with area A, and the magnetic field is constant with magnitude B, a simplified version of the formula can be used: Φ=B.A Cosθ If the surface is placed parallel to the magnetic field the area vector will form an angle of 90 degrees with the field and as a result the magnetic flux would be zero. If the surface is placed perpendicular to the field the area vector forms an angle of 0 with the field and hence the magnetic flux would be greatest. The integral of the magnetic flux through a surface S is defined as the integral of magnetic field over the area of the surface S. Φ=∫∫B.ds where is the magnetic flux B is the magnetic field, S is the surface (area) and '.' denotes the dot product,

### Magnetic flux through a closed surface

According to Gauss’s law of magnetism, the total magnetic flux through a closed surface is equal to zero. A closed surface is a surface like a sphere or disk. **Φ=∫∫B.ds=0** for any closed surface S.

### Magnetic flux through an open surface

In electromagnetism a magnetic flux passing through an open surface is of great importance. The **electromotive force** is produced when a changing magnetic flux is passes through a conductive coil. According to Faraday’s law: **E=-dφ/dt**, where E is the EMF, and the derivative is of Φ, the flux through a surface, with respect to time, T.

This is the principle on which an electrical generator works. Most common generators use the principal of magnetic flux to produce electricity. A changing magnetic flux induces emf in a coil. The emf causes the current to flow in the coil hence producing electricity.

### Measurement of Magnetic Flux

The apparatus used to measure magnetic flux is called a *fluxmeter*,it consists of coils and electronics which evaluate the voltage change in the coil to measure the magnetic flux.

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