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 L2 T-2 I-1]
Therefore, Magnetic Flux is dimensionally represented as [M1 L2 T-2 I-1].
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