Magnetic Flux

Magnetic Flux - Definition, Diagram, Formula, Solved Examples

The total number of magnetic field lines passing through a given coil or area is referred to as the Magnetic Flux. It is a component of the magnetic field that flows through the coil. Magnetic flux is denoted by ΦB where B is a magnetic field and Weber (Wb) is its unit. The magnetic flux value is a vector quantity that depends on the magnetic field direction.

 Magnetic Flux Formula

The magnetic flux formula is as follows:

Φ_B = BACosΘ

Φ_B = B.A

Where,

B = Magnetic field,

A =  Surface area and

Θ =  Angle between the magnetic field and normal to the surface.

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The Dimension of Magnetic Flux Density

• When compared to the magnetic flux of the body, the magnetic flux density is a different measure.
• The magnetic flux density is the quantity of magnetic flux per unit area considered perpendicular to the direction of magnetic flux.
• There is a relationship between the flux density (B) and the magnetic field (H).

It can be written as follows:

B = μH

• The magnetic flux density is measured in Webers per square metre. It is equivalent to Tesla (T).  
• The magnetic flux density (B) is defined further below. 
• It is the force exerted over a unit current per unit length on a wire held at an angle to the magnetic field.
• The dimension of Tesla (T) = kgs−2A-1

B is a vector quantity.

B = F/I1

Here, 

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 

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Dimensional Formula of Magnetic Flux

The dimensional formula of Magnetic Flux is given by,

[M1 L2 I-1 T-2]

Where,

M = Mass

I = Current

L = Length

T = Time

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How to Find Dimensional Formula?

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

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

Where,

 B = Magnetic Field,

 A = Surface Area, and

 = The angle formed by the magnetic field and the normal to the surface

The area dimensional formula = [M0 L2 T0].

Since, Force = Electric Charge × Magnetic Field × Velocity

Therefore, Magnetic Field = Force × [Electric Charge × Velocity]-1 . . . . . (2)

-> The dimensional formula of velocity = [M0 L1 T-1] . . . . . . . (3)

Since, charge = current × time

∴ The dimensional formula of electric charge = [M0 L0 I1 T1] . . . . . (4)

And, Force = M × a = M × [M0 L1 T-2]

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

On substituting equation (3), (4) and (5) in equation (2) we get,

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

Or, B = [M1 L1 T-2] × [M0 L0 I1 T1]-1 × [M0 L1 T-1]-1

As a result, the Magnetic Field dimensional formula is [M1 T-2 I-1]...

On substituting equation (6) in equation (1) we get,

Magnetic Flux = B × A × Cos θ

Or, Φ_B = [M1 T-2 I-1] × [M0 L2 T0] (Since, θ is Dimensionless Quantity)

Φ_B = [M1 L2 T-2 I-1]

Therefore, Magnetic Flux is dimensionally represented as [M1 L2 T-2 I-1].

Also Read:

Magnetic Flux Unit and Dimension

To calculate the magnetic flux, we must first assume the field-line image of a magnet or a system of magnets.

A perpendicular uniform magnetic field (= 900) is applied to a rectangular plate with area 'A.'

The magnitude of the magnetic field is B, and it 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 magnetic unit. It is also written in volt-second.