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

Φ_B = [M¹ L² T^-2 I^-1]

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

⇒ Check Other Dimensional Formulas:

• Dimensions of Coefficient of Friction
• Dimensions of Charge
• Dimensions of Reynolds Number
• Dimensions of Gravitational Potential Energy
• Dimensions of Linear Density