# How to calculate force from an electromagnet?

1. Sep 2, 2015

### senox13

Just what the title says, how do I calculate the force, in newtons, that an electromagnet would have on an object?

2. Sep 2, 2015

### Titan97

Force exerted on what?

3. Sep 2, 2015

### Hesch

The force is a result of change of the magnetic energy in the magnetic field.

Say you have a magnetic pole with a cross section area = A, and you close up some iron. Between the pole and the iron is an airgap, wherein there is a magnetic energy density, Edens.

Edens = ½ * B * H [ J/m3 ] , H is the magnetic field strength, B is the magnetic induction.

The volume of the airgap, Vairgap = A * s , where s is the distance between pole and iron, so the energy, E, in the airgap = A * s * ½ * B * H [ J ].

The force, F = dE / ds ≈ ½ * B * H * A [ N ], or to be more exact:

F = ( μr - 1 ) * ½ * B2 * A [ N ] , where μr is the relative permeability as for iron. So because μr = 1 as for wood, a magnet will not attract wood.

This formula is only valid when s is small compared to A.

You may say that the force is due to that airgap ( with high energy density ) is substituted by iron ( with lower energy density ) when iron closes up the pole. Thus magnetic energy is converted to mechanical energy, Emech = -F * Δs.

Last edited: Sep 2, 2015
4. Sep 2, 2015

### senox13

Okay, that was helpful, but what I'm trying to figure out is more of how much magnetic force I need to accelerate a slug of a certain mass to a certain speed. I assume there's an equation for this, but I have had little luck finding it with google.

5. Sep 2, 2015

### Staff: Mentor

Over what distance/time are you accelerating the slug?

6. Sep 3, 2015

### Hesch

The same magnetic force as for any other force: v(t) = a(t) dt = (F(t) / m) dt.

( Are you speaking of some linear motor ? )

Now, say that the system is digitally controlled, you could implement some look up table to linearize the force within some span of distance ( s ), thus keeping the force constant within this span, if desired.

7. Sep 3, 2015

### senox13

Instantantly, the coil should only be active for a fraction of a second. As for distance, as far as it'll go after leaving the coil or coils.

8. Sep 3, 2015

### Staff: Mentor

The equation relating acceleration and time is: A = (V - V0)/t, where V is the final velocity, V0 is the initial velocity, A is acceleration, and t is time.

The equation used to find the final velocity of an accelerating object is: V = V0 + At.

The equation relating force, mass, and acceleration is: F = MA

Note that in the first equation, setting t = 0 gives you a divide by zero error. In the second equation, t = 0 gives you zero change in velocity. This means that you have to have a non-zero time. Since the object only accelerates while a net force is applied (per the third equation), the force cannot be applied instantly. The time taken to accelerate the slug matters, even if it is only a fraction of a second.

There's really no easy way to figure this out if you don't know basic linear motion. There are several more equations that allow you to figure out the distance and time you need to apply the force over, but they aren't simply 'plug and play'. You have to know what each equation means and how to use and manipulate them. I highly recommend learning about basic linear motion, otherwise you'll just be floundering around in the dark. The best way would be to buy a used, college level physics textbook. I bought one for around 14 bucks from amazon, and I'm certain you can find cheaper ones. There's also plenty of websites and videos if you just search for 'basic linear motion' in google or youtube. I recommend the textbook, even if you plan to study mostly online. It will contain everything you need to know to learn about motion and will present it in an orderly fashion that makes it easier to learn. You're not bouncing around from site to site or video to video trying to figure out some concept.

Edit: Here's a physics book that's almost exactly like my own physics book and is only ten bucks used.

9. Sep 4, 2015

### senox13

Okay, allow me to rephrase myself because you seem to be assuming that my grasp of physics is nonexistent. I would have assumed that when you saw the phrase "fraction of a second," you would have understood that the word instantly was hyperbole. In doing slightly further research on electromagnets, which, admittedly, I knew very little about, I learned that although I don't need to fire the coils as precisely as I thought, though I still should try to have them active for as short a time as possible for the sake of power consumption. I suppose I should mention that this is all for a coilgun and I'm just trying to figure out how many coils and how much power I'll need to achieve the maximum possible muzzle velocity.

10. Sep 4, 2015

### Staff: Mentor

Nope. Clarity is important.

11. Sep 4, 2015

### senox13

Haha, okay, fair enough. But back to the topic, how possible is it to get a muzzle velocity of 100f/s from a one to two stage coilgun? Is this an unrealistic goal?

12. Sep 4, 2015

### Staff: Mentor

Before we get to that, do you know anything about basic electronics and electrical circuits?

13. Sep 4, 2015

### senox13

Eh, more or less. I know the equations and I've done my fair share of tinkering.