Engineers make solenoids – electromagnets – by twisting lengths of metal in a spiral fashion around a cylindrical template. You can determine the magnitude of that force by plugging the dimensions and other properties of the magnet based into a simple equation: F = (n X i)^{2} X magnetic constant X a / (2 X g^{2}). Passing an electrical current through the solenoid results in a magnetic field that exerts force on nearby ferromagnetic objects, such as pieces of iron or steel. The joining together of magnetic and electric forces on a charged item is called the Lorentz force.

Calculate the force by writing the equation:

F = (n x i)^{2} x magnetic constant x a / (2 x g^{2})

Where, F = force, i = current, g = length of the gap between the solenoid and a piece of metal, a = Area, n = number of turns in the solenoid, and the magnetic constant = 4 x PI x 10^{-7}.

Analyze your electromagnet to determine its dimensions and the amount of current you will be running through it. For example, imagine you have a magnet with 1,000 turns and a cross-sectional area of 0.5 neters that you will operate with 10 amperes of current, 1.5 meters from a piece of metal. Therefore:

N = 1,000, I = 10, A = 0.5 meters, g = 1.5 m

Plug the numbers into the equation to compute the force that will act on the piece of metal.

Force = ((1,000 x 10)^{2} x 4 x pi x 10^{-7} x 0.5) / (2 x 1.5^{2}) = 14 Newtons (N).