Question

Dimensional formula for inductance

Answer 1

Here i have given the way you can find dimension. Pls read carefully


Inductance is defined as
the ratio of Magnetic Flux to the current.

Inductance = Magnetic Flux / Current-------(1)

Magnetic Flux = Magnetic field × Area

Magnetic field = Force ⁄ current × Length............(since F = BIL)

Force = Mass × Acceleration

Acceleration = Velocity ⁄ Time

Velocity = Displacement / Time

Now we will start solving all the from the bottom i.e from the velocity

Displacement, Length = L & Time = T , Mass = M , Current = A

⇒ Velocity = Displacement / Time

Velocity = [ M L T−1]

⇒ Acceleration = Velocity ⁄ Time = [ M0 L T−1] ⁄ [T]

Acceleration = [M0 L T−2]

⇒ Force = Mass × Acceleration = [M] × [M0 L T−2]

Force = [M L T−2]

⇒ Magnetic field = Force ⁄ current × Length = [M L T−2] ⁄ [A × L]

Magnetic field = [M L0 T−2 A−1]

⇒ Magnetic Flux = Magnetic field × Area = [M L0 T−2 A−1] × [L2] ........(since Area = L × B = L2)

Magnetic Flux = [M L2 T−2 A−1]

⇒ Inductance = Magnetic Flux / Current = [M L2 T−2 A−1] ⁄ [A]

Inductance = [M L2 T−2 A−2]

Note:- Charge Q = Current × Time = [AT]

∴ Inductance = [M L2 Q−2] or [M L2 ⁄ Q2]