Dimensions of Magnetic Flux

The Dimension of Magnetic Flux

Electromagnetism is also among the subdivisions of the physics unit, which deals with the studying and analysis of the magnetic field caused by the electric field for many other reasons. 

Let’s just define the magnetic flux over an external part (surface) of the body. 

The magnetic flux is the surface-integral of the usual component of the magnetic field (B), which moves through that surface. 

The symbol which is used to denote the magnetic flux is ‘Φ’ or ‘ΦB’. 

Maxwell is the centimeter–gram–second (CGS) system of the unit for magnetic flux.

Wb or Weber is the SI unit of magnetic flux. 

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Do you know about the Magnetic Flux?

In simple terms, the magnetic flux is defined as the measurement of the sum of the magnetic field which travels through a selected area. Otherwise, it can be stated as the amount of magnetic field lines transient through a specified closed superficial. 

The magnetic flux deals with the calculation of the total amount of magnetic field that is passing through the body’s surface.

In this case, we can consider the area of any size, as well as its orientation, is independent according to the direction of the magnetic field. 

The dimensional formula of Magnetic Flux can be represented as [M1 L2 I-1 T-2]

In this dimension,

  • I = Current

  • L = Length

  • M = Mass

  • T = Time


The Dimension of Magnetic Flux Density

The magnetic flux density is a different measure as compared to the magnetic flux of the body.

The quantity of magnetic flux via unit area is considered as perpendicular to the direction of magnetic flux, known as the magnetic flux density.

There is a relation between the flux density (B), and the magnetic field (H).

It can be given as:

B = μH

The measurement of the magnetic flux density is in Webers per square meter. It is correspondent to Tesla (T).  

The definition of the magnetic flux density (B) is explained below. 

It is the force applying over unit current per unit length on a wire kept at the right angle to the magnetic field.

The dimension of Tesla (T) = kgs−2A-1

B is a vector quantity.

B = \[\frac{F}{I1}\]

Here, 

F = total force acting on the wire 

I = current flowing through the wire 

l = length of wire 

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[MT−2L0A−1] is the dimensional formula of magnetic flux density 


How to Find Dimensions of Magnetic Flux?

Let’s have just derived the dimension of magnetic flux

We know that:

ΦB = Magnetic Flux = B × A × Cos θ-------(1)

Here, 

B = Magnetic Field 

A = Surface Area

θ = Angle between the normal to the surface and magnetic field 

We also know,

[M0 L2 T0] = the dimensional formula of area 

Here,

Electric Charge × Magnetic Field × Velocity = Force

∴ Force × [Electric Charge × Velocity]-1 = Magnetic Field-------(2)

⇒ [M0 L1 T-1] = the dimensional formula of velocity---------(3)

As per our knowledge, 

Charge = current × time

∴ [M0 L0 I1 T1] is the dimensional formula of electric charge--------(4)

Also,

M × a = M × [M0 L1 T-2] = Force

∴ [M1 L1 T-2] = The dimensional formula of force---------(5)

If we replace the equations (3), (4) and (5) in equation (2) we acquire,

Force × [Charge × Velocity]-1 = Magnetic Field 

⇒ [MLT-2] × [M0 L0 I1 T1]-1 × [M0 L1 T-1]-1 = B

We concluded that [M1 T-2 I-1] is the dimensional formula of Magnetic Field------------(6)

By replacing the equation (6) in equation (1) we achieve,

B × A × Cos θ = Magnetic Flux  

⇒ ΦB = [M1 T-2 I-1] × [M0 L2 T0] (θ = Dimensionless Quantity)

⇒ [M1 LT-2 I-1] = ΦB ---------(Proved)


Unit and Dimension of Magnetic Flux 

Sir Michael Faraday explained a perfect mathematical relation for clarifying on the magnetic flux. 

It helped him to get the relation due to the modes of experiments that were performed by him on electromagnetic induction. 

The total credit regarding the concept of magnetic flux goes to Michael Faraday as he played an important role in accumulating all the relations in electromagnetism.  

These relations have multiple usages in electromagnetic induction.

For calculating the magnetic flux, we need to assume that the field-line image of a magnet or the system of magnets. This is shown in the image below. 

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A rectangular plate of the area ‘A’ is placed under the influence of the perpendicular uniform magnetic field (\[\Theta\] = 90⁰).

The magnetic field's magnitude is B and is a scalar product.

[M1 L2 T2 I1] = The SI unit and dimension of the magnetic flux.

In this dimension 

M = mass 

L = length 

T = time 

I = electric current 

Weber is the SI derived unit of magnetic. It is also written in volt-second.

FAQs (Frequently Asked Questions)

Q1. What is the Dissimilarity Between the Magnetic Flux and the Magnetic Field?

Ans: The dissimilarity between the magnetic flux and the magnetic field is given below.

We know that the area near the magnet where the motion of charge feels a force is called the magnetic field.

However, in the case of the magnetic flux, it visualizes the amount of force of magnetic lines generated by the magnet.

Q2. Explain about the Two Kinds of the Magnetic Pole.

Ans: There are two kinds of magnetic poles seen, such as the north-seeking pole. It is found in a magnet and also called a north magnetic pole. 

The other one is the south-seeking pole found just opposite to the north-pole. It is also found in a magnet and named as a south magnetic pole. 

Different poles attract each other, just like different magnets. Similar poles repel each other.

Q3. Explain the Factors that Affect the Magnetic Field.

Ans: There are several factors that affect the strength of the magnetic field, such as 

  1. Core material’s nature

  2. The current’s strength traveling through the core

  3. The number of rounds of wire on the core 

  4. The structure (shape and size) of the core

Q4. Calculate the Magnetic Flux of the Wire Producing a Force of 440 N of a Length 20m. The Current in the Wire is 2A.

Ans: Data given here are:

Force-induced in the wire F = 440 N

Length of the wire (l) = 20m

Current in the wire (I) = 2A

The magnetic flux B = F/I1 = 440/(20 * 2) = 11 Tesla

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