Dimensional Formula of Magnetic Field

The dimensional formula of Magnetic Field is given by,

M¹ T^-2 I^-1

Where,

• M = Mass
• I = Current
• L = Length
• T = Time

Derivation

Since, Lorentz Force (F) = Charge × Magnetic Field (B) × Velocity

Therefore, Magnetic Field (B) = Lorentz Force × [Charge × Velocity]^-1 . . . . . (1)

Since, Velocity = Distance × Time^-1

∴ The dimensional formula of velocity = [L T^-1]. . . . . . . (2)

Since, electric charge = electric current × time

∴ The dimensional formula of electric charge = [I¹ T¹] . . . . . (3)

And, Lorentz Force = Mass × Acceleration = M × [L T^-2]

∴ The dimensional formula of Lorentz Force = M¹ L¹ T^-2 . . . . (4)

On substituting equation (2), (3) and (4) in equation (1) we get,

Magnetic Field = Force × [Charge × Velocity]^-1

Or, B = [M¹ L¹ T^-2] × [I¹ T¹]^-1 × [L T^-1]^-1 = [M¹ L⁰ T^-2 I^-1].

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

⇒ Check Other Dimensional Formulas:

• Dimensions of Velocity
• Dimensions of Momentum
• Dimensions of Dipole Moment
• Dimensions of Impedance
• Dimensions of Universal Gas Constant