1Which of these has the same dimensions as mutual inductance?
Mutual inductance and self inductance both have the dimensions [M L² T⁻² A⁻²].
Induction, AC and EM wavesClass 12, Electromagnetic Induction
Dimensional formula of Mutual inductance
[M L2 T-2 A-2]
Flux linked with one coil per unit current in a neighbouring coil. It has the same dimension as self inductance.
How to get the dimensional formula of mutual inductance
- Start from the definition: mutual inductance = magnetic flux / electric current.
- 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].
- magnetic field = force / (electric charge × velocity), so magnetic field is [M L T-2] / ([T A] × [L T-1]) = [M T-2 A-1].
- area = length × length, so area is [L] × [L] = [L2].
- Put in the dimension of each part: [M L2 T-2 A-1] / [A].
- Add the powers of each base quantity: [M L2 T-2 A-2].
Quantities with the dimensions [M L² T⁻² A⁻²]
Equal dimensions do not make them the same quantity. Compare mutual inductance with the others in the full grid.
Three questions on mutual inductance
2What is the SI unit of mutual inductance?
The SI unit of mutual inductance is the henry (H).
3Do mutual inductance and Poynting vector have the same dimensions?
Mutual inductance is [M L² T⁻² A⁻²] but Poynting vector is [M T⁻³].
Mutual inductance: quick answers
What is the dimensional formula of mutual inductance?
The dimensional formula of mutual inductance is [M L² T⁻² A⁻²]. It comes from mutual inductance = magnetic flux / electric current.
What is the SI unit of mutual inductance?
The SI unit of mutual inductance is the henry (H).
Which quantities have the same dimensions as mutual inductance?
Mutual inductance shares [M L² T⁻² A⁻²] with self inductance. Equal dimensions do not make them the same quantity.