# Magnetomotive Force

Definition: Magnetomotive force (MMF) is the magnetic pressure that sets up the magnetic flux in the magnetic circuit. Without MMF, it is not possible to set up flux in the magnetic circuit. The MMF in a magnetic circuit is analogous to the electromotive force in an electric circuit.

The electromotive force accelerates the electrons and thus the current flows in the electric circuit. Similarly, the MMF set up flux in the magnetic circuit. The magnitude of the flux in a magnetic circuit depends on the magnetomotive force and the reluctance of the magnetic circuit. The MMF of the magnetic circuit depends on the number of turns in a coil and the magnitude of the current. We denote the MMF by the letter F.

### Formula of MMF

The formula of MMF is given below.

F = NI

Where N- Number of turns and I is the current

### Unit of MMF

The SI unit of the MMF is Ampere-turn (AT) & its CGS unit is G (gilbert).

Let us understand the meaning of MMF by taking an example of a coil wound on magnetic material.

## Magnetomotive Force of Inductive Coil

The MMF for the inductive coil shown in the figure below is expressed as

Where, N – numbers of turns of the inductive coil
I – current

The strength of the MMF is equal to the product of the current flowing in a coil and the number of turns. The work is done in moving the unit magnetic pole(1 weber) in a magnetic circuit.

MMF is the magnetic potential that sets up the flux in the magnetic circuit.

Flux = MMF/ Reluctance

MMF = Flux X Reluctance

F= Φ X Rm

The opposition offered by a magnetic material is the magnetic reluctance.

## Solved Problems on MMF

A coil of 100 turns is wound uniformly over a wooden ring that carries a 2-ampere current. Calculate MMF?

F = NI
= 100 x 2
= 200 AT

Calculate the magnetomotive force required to produce a flux of 0.020 Wb
across an air-gap 2.0 mm long, having an effective area of 200 cm2

ϕ = 0.020 Wb, l = 2.0 mm = 2.0×10-3 m, A = 200 cm2 = 2×10-2 m2
B = ϕ / A
= 0.020 / (2×10-2)
= 1 T
H = B / μ0
=1 / (4π×10-7)
= 7.96×105 A/m
F (MMF) = H.l = 7.97×105 × 2.0 ×10-3 = 1.59×103 AT