# Magnetomotive force and the H-field

## Homework Statement

The magnetomotive force is given as an integral of the H-field. I want to know how this can be a force.

## Homework Equations

$$\int H \cdot d \ell = F$$

## The Attempt at a Solution

So a bit confused. Wiki says that this equation

$$\int H \cdot d \ell = F$$

is a force, the magneto-motive-force. But this is the H-field multiplied by a length $$\ell$$. From what I knew about the H-field, if you multiply the H-field with a length, you should get a current, not a force as

$$\int H \cdot d\ell = I$$

I know this because

$$H = \frac{I}{2\pi r}$$

you can see why by rearranging it

$$H \cdot r = \frac{I}{2\pi}$$

so what gives?