What is Magnetic Flux | Physics for EmSAT Achieve PDF Download

In the realm of electromagnetism, a branch of physics, the magnetic flux across a surface represents the integral of the magnetic field's normal component (B) passing through that surface. This quantity is typically symbolized by Φ or Φ_B. The CGS unit for magnetic flux is the Maxwell, while the SI unit is the Weber (Wb).

What is Magnetic Flux?

Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. It provides 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.

Magnetic Flux Symbol

• Magnetic flux is commonly denoted using the Greek letter Phi or Phi suffix B.
• Magnetic flux symbol: Φ or Φ_B.

Magnetic Flux Formula

Magnetic flux formula is given by:

Where,

• Φ_B is the magnetic flux.
• B is the magnetic field
• A is the area
• θ the angle at which the field lines pass through the given surface area

Magnetic Flux Unit

Magnetic flux is usually measured with a flux meter. The SI and CGS unit of magnetic flux is given below:

• The SI unit of magnetic flux is Weber (Wb).
• The fundamental unit is Volt-seconds.
• The CGS unit is Maxwell.

Understanding Magnetic Flux

• Faraday's significant breakthroughs stemmed from his quest to establish a straightforward mathematical relationship that could elucidate the series of experiments he conducted on electromagnetic induction. Widely acclaimed as the preeminent experimental scientist of the nineteenth century, Faraday made numerous profound contributions to the field of science. 
• Before delving into an appreciation of his work, it's imperative to grasp the concept of magnetic flux, which plays a pivotal role in electromagnetic induction.
• To compute magnetic flux, one considers the depiction of field lines from a magnet or a system of magnets, as illustrated below. The magnetic flux passing through a plane with an area represented by A, positioned within a uniform magnetic field with a magnitude denoted by B, is calculated as the scalar product of the magnetic field and the area A. 
• The angle at which the field lines intersect the given surface area is crucial. When the field lines meet the area at a shallow angle, specifically when the angle between the magnetic field vector and the area vector approaches 90ᵒ, the resulting flux is minimal. Conversely, when this angle equals 0ᵒ, the resulting flux reaches its maximum value.

Mathematically,
Where θ is the angle between vector A and 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,

It is clear from the equation given above that the magnetic flux is a scalar quantity. 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. 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 event of changing magnetic field reading over an area, it would be necessary to find the average reading. 

What is 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 = F/Iℓ
Where, l = length of wire, F = total force acting on the wire, and I = current flowing through the wire.

Magnetic Flux Density Unit

The CGS and SI unit of magnetic flux density is given in the table below.