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
From the above formula, the dimensions of Φ are (1, 2, -2, -1) in terms of mass, length, time, and ampere (current).
The dimensional equation of magnetic flux is
Φ = [ M1 L2 T-2 A-1 ]
Here, Φ is the symbol of magnetic flux.
- Dimensional Formula of Magnetic Field
- Dimensional Formula of Electric Flux