The dimensional formula of Magnetic Flux is

**[ M**^{1}** L**^{2}** 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 / time
^{2}

After substituting the value of **acceleration**, our formula becomes

```
Magnetic Field (Φ) = (mass * displacement / time
```^{2} ) / (Current * length)

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

```
Φ = ((mass * displacement / time
```^{2} ) / (Current * length)) * surface area
= (mass * displacement * surface area ) / (Current * length * time^{2})

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

```
Φ = (mass * displacement * length * breadth) / (current * length * time
```^{2})
= (mass * displacement * breadth) / (current * time^{2})
= 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 = [M
```^{1}] * [L^{1}] * [L^{1}] * [A^{-1}] * [T^{-2}]
= [M^{1}] * [L^{2}] * [T^{-2}] * [A^{-1}]

Hence, the dimensional formula of magnetic flux is **[ M**^{1}** L**^{2}** 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 = [ M ^{1} L^{2} T^{-2} A^{-1}**

**]**

Here, Φ is the symbol of magnetic flux.

**Related Articles**

*Dimensional Formula of Magnetic Field**Dimensional Formula of Electric Flux*