Weber - Meaning, Definition, Dimension, and FAQs

In the 19th century, the Weber unit of magnetic flux was named as an honour to a German Physicist named Wilhelm Eduard Weber (1804-1891). Weber is the unit of magnetic flux that causes the electromotive force of one volt in a circuit of one rotation when generated/removed in one second.

In terms of Faraday’s law, the SI unit of flux is Weber, it is related to a changing magnetic flux through a loop to the electric field around the loop. A change in flux of one weber per second induces an electromotive force of one volt, or it produces an electric potential difference of one volt across two open-circuited terminals.

What is Magnetic Flux?

In this article, we will understand the flux definition with various flux units in detail. Do you know what flux is and what is the SI unit of magnetic flux? Well, flux is the number of magnetic field lines passing through a cross-sectional area perpendicularly.

Flux Definition: 

A magnetic flux is the product of the average magnetic field and the perpendicular area that it penetrates. 

In mathematical terms, we can reinstate the above statement as

ɸ = B.A,

Where ɸ = magnetic flux, where the unit of magnetic flux is Weber (Wb) or Tesla metre squared or (Tm2).

Here, Tesla is equal to Weber per metre square. It is also the unit of flux density. 

B = Magnetic field strength. It is measured in SI base units of Ampere per metre or A/m. Also, A = perpendicular area through which magnetic field lines cross.

So, the magnetic flux depends on both the magnetic strength and the area.

We can see the dot product of B and A. Here, we can rewrite the above equation as

ɸ = B.A Cosθ

Here,

Cosθ = The angle between the planar area and the magnetic flux.

Magnetic Flux

Faraday’s awesome insights lay the foundation for finding a simple mathematical relation to elaborate the explanation of the series of experiments that he conducted on electromagnetic induction (EMI). Faraday made several contributions to science (especially in magnetism) and till present, he is widely known as the greatest experimental scientist of the nineteenth century. Before we start appreciating his great works, let us understand the concept of magnetic flux, which plays a major role in EMI.

For calculating the magnetic flux, we consider the field-line image of a magnet/the system of magnets, as shown in the image below:

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In this image, we can see that the magnetic flux crosses a planar area indicated by the letter ‘A’ that is placed in a uniform magnetic field of magnitude given by B (which is actually the magnetic field strength). 

The product of these two quantities, viz. B and A, is given as the scalar product of these. The angle (Cosθ), at which the field lines pass through the given surface area, plays a significant role here. The field lines here intersect the area at a certain angle, that is:

• When the angle between the magnetic field vector B→ and the area vector A is nearly equal to or equal to 90°, the resulting flux is very low or zero, respectively.

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• When the angle is equal to 0°, the resulting flux is maximum.

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Points to Ponder:

Magnetic flux is a quantity of convenience in Faraday's Law statement and in the explanation of objects like transformers and solenoids.

Dimension of Weber

In the practical metre-kilogram-second (MKS), the SI unit of magnetic flux is equal to that flux in which an armature of one turn produces in it an electromotive force of one volt as soon as the flux is reduced to zero at a uniform rate, in one second.

Since we know that the SI unit of magnetic flux is Weber we can express Weber in terms of derived units as Joules per ampere or J/A,

Where one Weber = One V·s = 1 (Tm2) = 1 J/A.

So, the unit of weber is kgm2s-2A-1, and

The dimension of Weber is [ML2T-2A-1].

Points to Note:

• In the CGS system of units, a.k.a. Centi-Gram-Second, one Weber is equal to 108 Maxwells.

• The two flux units are Weber and Maxwell.

Weber Number

Weber's number was named after a professor of naval mechanics at the Polytechnic Institute of Berlin, named Moritz Weber (1871–1951).

The Weber number (We) is a dimensionless number employed in the field of fluid mechanics. Weber number is often useful in analysing fluid flows whenever there is an interface between two different fluids, especially for fluids with multiphase flowing with strongly curved surfaces.

Magnetic Flux Density is the amount of magnetic flux flowing through a unit area and is perpendicular to the direction of magnetic flux. Magnetic flux density is denoted by B and is related to the magnetic field denoted by H, as follows:

B = 𝜇H, where 𝜇 =  magnetic permeability. 

It is measured in Weber per metre square, which is equal to Tesla.

The SI unit of magnetic flux density is Tesla, denoted by T. It is an SI unit that measures the strength and the direction of the magnetic field flowing through any area. 

Magnetic flux density is calculated near the poles of the magnet, where the magnetic field is highest and the region as compared to others is lowest. The usual direction of the flow of magnetic flux is from the north pole to the south pole.

How to calculate Magnetic Flux Density? 

• To determine any magnetic flux density, first, the total magnetic flux should be calculated, which is generated from the magnetic field. 

• The second step is to measure the total area on which the flux is acting. 

• To find the flux density, divide the total flux by the total area. 

Quick Summary

To summarise the entire topic, below given is a quick revision table representing all the important concepts related to Weber.

Did you know?

• The first discovery relating to the field of magnetism and magnet was by Nikola Tesla.

• The earth’s magnetic field is 1000 times less than that of a bar magnet.

• In the solar system, there are only five planets having magnetic fields, which are Earth, Jupiter, Saturn, Neptune, and Uranus.

• Neptune has the strongest magnetic field.

• The earth’s magnetic poles move about 40 km each year.

Solved Question 

1. Determine the magnetic flux through a field that has a length of 0.50 m and a breadth of 0.60 m, where a magnetic field of 0.02 T is applied to an angle of 45o.

Solution:

According to the given problem, the magnetic field is 0.02 T at an angle of 45o. 

So, B = 0.02 T and 𝛉 = 45o 

And dimensions of the field are given as 0.50 m and 0.60 m. 

Magnetic flux is given by

ɸB = B.A 

I.e. ɸB = B A cos𝛉 

ɸB = 0.02 x 0.50 x 0.60 x cos45

ɸB = 0.00312 Wb 

Therefore, magnetic flux is 0.00312 Wb.