# Magnetic Flux

Faraday’s great insights lay on finding a simple mathematical relation to explain the series of experiments that he conducted on electromagnetic induction. Faraday made numerous contributions to science and is widely known as the greatest experimental scientist of the nineteenth century. Before we start appreciating his work, let us understand the concept of magnetic flux which plays a major part in the electromagnetic induction

## Magnetic Flux:

It is defined as the number of magnetic field lines passing through a given closed surface. It gives the measurement of the total magnetic field that passes through a given surface area. Here, the area under consideration can be of any size and under any orientation with respect to the direction of the magnetic field.

In order to calculate the magnetic flux, we consider the field-line image of a magnet or the system of magnets, as shown in the image below. The magnetic flux through a plane of the area given by A that is placed in a uniform magnetic field of magnitude given by B is given as the scalar product of the magnetic field and the area A. Here, the angle at which the field lines pass through the given surface area is also important. If the field lines intersect the area at glancing angle, that is, when the angle between the magnetic field vector and the area vector is nearly equal to 90ᵒ, then the resulting flux is very low, whereas, when the angle is equal to 0ᵒ, the resulting flux is maximum.

Mathematically,

$\phi _{B}=B.A=BA\; cos \; \Theta$

Where θ is the angle between the vector A and the vector B.

If the magnetic field is non-uniform and at different parts of the surface, the magnetic field is different in magnitude and direction, then the total magnetic flux through the given surface can be given as the summation of the product of all such area elements and their corresponding magnetic field. Mathematically,

$\phi _{B}=B_{1}.dA_{1}+B_{2}.dA_{2}+B_{3}.dA_{3}+…= \sum_{all}^{} B_{i}.dA_{i}$

It is clear from the equation given above that the magnetic flux is a scalar quantity and its SI unit is given as Weber (Wb) or tesla meter squared (Tm2).

## Measurement of Magnetic Flux

The SI unit of magnetic flux is Weber (Wb) or tesla meter squared (Tm2) named after German physicist  Wilhelm Weber. A magnetic flux can be measured with a magnetometer. Suppose a probe of the magnetometer is moved around an area of 0.6 m2  near a large sheet of magnetic material and indicates a constant reading of 5 mT. Then the magnetic flux through that area is calculated as ( 5 ×10-3 T) ⋅ (0.6 m2 ) = 0.0030 Wb. In the events of changing magnetic field reading over an area, it would be necessary to find the average reading.

## Magnetic Flux Density

Magnetic flux density (B) is defined as the force acting per unit current per unit length on a wire placed at right angles to the magnetic field.

• Units of  B is Tesla (T) or $Kgs^{-2}A^{-1}$
• B is a vector quantity

$B=\frac{F}{Il}$

Where,

$l$=length of wire

$F$=total force acting on the wire

$I$=current flowing through the wire