# Dimensions of Magnetic Field

## 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 = [MLT-2] × [I1 T1]-1 × [L T-1]-1 = [M1 LT-2 I-1].

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

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