# 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.

Related Articles

• Dimensional Formula of Magnetic Field
• Dimensional Formula of Electric Flux