1Which is the dimensional formula of magnetic field?
Magnetic field works out to [M T⁻² A⁻¹].
MagnetismClass 12, Moving Charges and Magnetism
Dimensional formula of Magnetic field
[M T-2 A-1]
From F = qvB, force per unit charge and speed. One tesla is one newton per ampere metre.
How to get the dimensional formula of magnetic field
- Start from the definition: magnetic field = force / (electric charge × velocity).
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
- Put in the dimension of each part: [M L T-2] / ([T A] × [L T-1]).
- Add the powers of each base quantity: [M T-2 A-1].
Three questions on magnetic field
2What is the SI unit of magnetic field?
The SI unit of magnetic field is the tesla (T).
3Do magnetic field and magnetic moment have the same dimensions?
Magnetic field is [M T⁻² A⁻¹] but magnetic moment is [L² A].
An equation that uses magnetic field
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
F = q v B sin(θ)F[M L T-2]=q v B sin(theta)[M L T-2]Dimensionally consistentEvery term is [M L T-2]
v = velocityθ = angle
Magnetic field: quick answers
What is the dimensional formula of magnetic field?
The dimensional formula of magnetic field is [M T⁻² A⁻¹]. It comes from magnetic field = force / (electric charge × velocity).
What is the SI unit of magnetic field?
The SI unit of magnetic field is the tesla (T).
Is magnetic field dimensionless?
No. Magnetic field has the dimensions [M T⁻² A⁻¹].