# Dimensions of Magnetic Flux

## 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

### Derivation

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

Where, B = Magnetic Field, A = Surface Area, and θ = Angle between the magnetic field and normal to the surface.

The dimensional formula of area = [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

Therefore, the dimensional formula of Magnetic Field is [M1 T-2 I-1] . . . . . (6)

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

Magnetic Flux = B × A × Cos θ

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

ΦB = [M1 LT-2 I-1]

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

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