Dimensional Formula of Magnetic Flux

The dimensional formula of Magnetic Flux is 

[ M1  L2  T-2 A-1]

where [M], [L], [T], and [A] are the fundamental quantities: Mass, Length, Time, and Ampere (Current).

Now let’s see how we can drive this formula.

How to calculate the dimensional formula of magnetic flux?

The mathematic formula of magnetic flux is,


  Magnetic Flux (Φ) = Magnetic Field * surface area

We know that in a magnetic field, the force on a wire with current I and length L is given by,


  Force = Current * length * Magnetic Field

  Magnetic Field = Force / (Current * length)

The formula of Force is mass * acceleration, so substituting this value in the above equation, we get


  Magnetic Field = (mass * acceleration) / (Current * length)

Also, we can further derive acceleration.

  • acceleration = speed / time
  • speed = displacement / time
  • acceleration = displacement / time2

After substituting the value of acceleration, our formula becomes


  Magnetic Field (Φ) = (mass * displacement / time2 ) / (Current * length)

Let’s use the value of the magnetic field in our earlier equation,


  Φ = ((mass * displacement / time2 ) / (Current * length)) * surface area

      = (mass * displacement * surface area ) / (Current * length * time2)

Further simplifying the surface area to length * breadth, we get


  Φ = (mass * displacement * length * breadth) / (current * length * time2)

     = (mass * displacement * breadth) / (current * time2)

     = mass * displacement * breadth * current-1 * time-2

Dimensionally, we use

  • [M] to represent mass
  • [L] for displacement and breadth
  • [T] to represent time
  • and [A] for current

Now our formula becomes,


  Φ = [M1] * [L1] * [L1] * [A-1] * [T-2]

      = [M1] * [L2] * [T-2] * [A-1]

Hence, the dimensional formula of magnetic flux is [ M1 L2 T-2 A-1 ].

Frequently Asked Questions

1. What are the dimensions of magnetic flux?

From the above formula, the dimensions of Φ are (1, 2, -2, -1) in terms of mass, length, time, and ampere (current).

2. What is the dimensional equation of Φ?

The dimensional equation of magnetic flux is

Φ = [ M1 L2 T-2 A-1 ]

Here, Φ is the symbol of magnetic flux.

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  • Dimensional Formula of Electric Flux