Question

Hello. My question is what is the equation of magnetic attraction force to iron? How it will lead to that equation?

Answer 1

The magnetic force to iron will be:

The equation is  F=(NI)² U0A/2g²

where This equation gives the force in Newtons of an electromagnet given the number of turns in the electromagnetic coil (N),

the current flowIng through the electromagnet (I),

the magnetic permeability of a vacuum (U0),

the cross-sectional frontal area of the ferromagnetic material (A),

the distance of the ferromagnetic material (g).

The units for A and g are arbitrary, as long as you're consistent with the usage. F will always be in Newtons, and ?0 is a constant of nature (sometimes called the magnetic constant).

how it will lead to that equation

Now consider

Now consider the energy density of particular field inside the air gap is uniform, we can calculate the total field energy of that gap by volume of the field

V = g × A
where g is the gap length and A is the cross sectional area of the coil's core.

The total energy is then

W = ((NI)²/2 U0)×g×A

W=   (B²/2 U0)×g×A

We need the force on the armature. That is given by the rate of change of energy with gap length

F = dW/dg

F = B² A / (2 U0)

We next need to find the flux density, B. It's assumption time again. Well designed relays use such high permeability material for the core and armature that most of the field strength produced by the coil will appear across the air gap between the core and the armature and we can ignore the reluctance of the core, pivot and armature.

B = F_m U0 / g

In this way by putting value of B in the above equation you will get the force equation.