# Magnetomotive Force (MMF) and Ampere-Turns with Solved Problems

- Link: https://studyelectrical.com/2024/03/magnetomotive-force-ampere-turns.html
- Published: 2024-03-16T18:23:03+00:00
- Author: Tesla

**Definition**: The magnetomotive force (MMF) is defined as the work done in moving
a unit magnetic pole once around the magnetic circuit. It is measured in ampere-
turns.

Magnetomotive force (MMF) is like the pressure that makes magnetic flux happen in
a magnetic circuit. Without MMF, there can’t be any flux in the magnetic circuit.
MMF in a magnetic circuit is similar to [electromotive force](https://studyelectrical.com/2017/04/electric-potential-difference-and-emf.html)
in an electric circuit.

## What is Magnetomotive Force?

The product of current and turns, known as IN, denotes the **magnetizing force**
or **magnetic potential**, termed as **magnetomotive force (mmf)**.

![magnetomotive force mmf](https://studyelectrical.com/wp-content/uploads/2024/03/
magnetomotive-force-mmf.webp)

Magnetomotive force mmf

The magnetic field strength of a coil magnet is influenced by the amount of current
flowing through its turns.

More current flowing through the coil leads to a stronger magnetic field. Additionally,
having more turns in a specific length concentrates the magnetic field.

The coil, resembling a bar magnet, possesses opposite poles at its ends, resulting
in a magnetic field proportional to the ampere-turns.

The magnetomotive force (MMF) drives or tends to drive flux through a magnetic circuit
and corresponds to electromotive force (EMF) in an electric circuit. Magnetomotive
force is equal to the work done in joules in carrying a unit magnetic pole once 
through the entire magnetic circuit.

In fact, as potential difference between any two points is measured by the work 
done in carrying a unit charge from one points to another, similarly, mmf between
two points is measured by the work done in joules in carrying a unit magnetic pole
from one point to another.

## MMF Equation

This relationship is expressed as:

**MMF = Current (I) × Number of Turns (N)**

where I is the current in amperes and N is number of turns.

#### Practical Unit: Ampere-turn

The practical unit for measuring magnetomotive force is the ampere-turn, abbreviated
as AT. This unit reflects the combined effect of current and turns in a coil.

![MMF equation 2](https://studyelectrical.com/wp-content/uploads/2024/03/MMF-equation-
2.webp)

MMF = N x I = 10 x 1 = 10 AT

![MMF equation 1](https://studyelectrical.com/wp-content/uploads/2024/03/MMF-equation-
1.webp)

MMF = N x I = 5 x 2 = 10 AT

Two examples of equal ampere-turns for the same mmf are shown above. A solenoid 
with 5 turns and 2 amperes exhibits the same magnetizing force as one with 10 turns
and 1 ampere, as the product of amperes and turns remains consistent.

Utilizing thinner wire allows for more turns to be accommodated within a given space,
influencing the magnetic field strength. The amount of current flowing through the
coil depends on the wire’s resistance and the source voltage.

The required number of ampere-turns depends on the desired magnetic field strength.
Adjustments in current or turns can be made accordingly.

## Units of Magnetomotive Force

The ampere-turn, AT, is an SI unit. It is calculated as NI with the current in 
amperes.

The cgs unit of mmf is the **gilbert**, abbreviated **Gb**.

One ampere-turn equals 1.26 Gb. The number 1.26 is approximately 4π/10, derived 
from the surface area of a sphere, which is 4πr^(2).

To convert IN to gilberts, multiply the ampere-turns by the constant conversion 
factor 1.26G/1 AT.

As an example, 1000 AT is the same mmf as 1260 Gb. The calculations are 1000 AT 
× 1.26 Gb/1 AT = 1260 Gb. Note that the units of AT cancel in the conversion.

| Description | Information | 
| Ampere-turn (AT) | SI unit for magnetomotive force | 
| Calculation | AT = I × N | 
| cgs unit of mmf | Gilbert (Gb) | 
| Conversion factor | 1 AT = 1.26 Gb | 
| Conversion to gilberts | Multiply AT by 1.26 Gb | 
| Example conversion | 1000 AT = 1260 Gb |

## Solved Example Problems

**Example 1**

Calculate the ampere-turns of mmf for a coil with 2000 turns and a 5-mA current.

**Solution**:

To calculate the ampere-turns (AT) of magnetomotive force (mmf) for a coil with 
2000 turns and a 5-mA (0.005 A) current, we can use the formula:

$\text{AT} = I \times N $

Where:

 * ( I ) = Current in amperes
 * ( N ) = Number of turns

Given:

 * I = 0.005 A
 * N = 2000 turns

Substituting the values:

$\text{AT} = 0.005 \, \text{A} \times 2000 \, \text{turns} $

$ \text{AT} = 10 \, \text{A-turns} $

So, the ampere-turns of mmf for the given coil is 10 A-turns.

**Example 2**

To find the number of turns required for a coil to provide a magnetizing force of
600 A?t with a current of 4 A, we can rearrange the formula for ampere-turns:

$ \text{AT} = I \times N $

Given:

 * AT = 600 ) AT
 * I = 4 A

We rearrange the formula to solve for ( N ):

$ N = \frac{\text{AT}}{I} $

Substituting the given values:

$ N = \frac{600 \, \text{A?t}}{4 \, \text{A}} $

$ N = 150 \, \text{turns} $

Therefore, 150 turns are necessary for the coil to provide a magnetizing force of
600 AT with a current of 4 A.

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