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 centimetre–gram–second (CGS) system of the unit for magnetic flux.
Wb or Weber is the SI unit of magnetic flux.
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, 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 metre. It is corresponding 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 = F/I1
F = total force acting on the wire
I = current flowing through the wire
l = length of wire
[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)
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
Electric Charge × Magnetic Field × Velocity = Force
∴ Force × ElectricCharge×Velocity (ElectricCharge×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)
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 (Charge×Velocity)-1 = Magnetic Field
⇒ [M1 L1 T-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 L2 T-2 I-1] = ΦB ---------(Proved)
Unit and Dimension of Magnetic Flux
Sir Michael Faraday explained a perfect mathematical relation for clarifying 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 the field-line image of a magnet or the system of magnets.
A rectangular plate of the area ‘A’ is placed under the influence of the perpendicular uniform magnetic field (Θ = 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.
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