Editing Electromagnet (section)

=== Force exerted by magnetic field ===
Likewise, on the solenoid, the force exerted by an electromagnet on a conductor located at a section of core material is:
{{NumBlk|:|<math>F = \frac{B^2 A}{2 \mu_0} </math>|{{EquationRef|2}}}}

This equation can be derived from the [[Magnetic energy|energy stored in a magnetic field]]. [[Energy]] is force times distance. Rearranging terms yields the equation above.

The 1.6&nbsp;T limit on the field<ref name="Pauley" /><ref name="Short" /> previously mentioned sets a limit on the maximum force per unit core area, or [[magnetic pressure]], an iron-core electromagnet can exert; roughly:

:<math>\frac{F}{A} = \frac {(B_\text{sat})^2}{2 \mu_0}  \approx 1000\ \mathrm{kPa} = 10^6 \mathrm{N/m^2} = 145\ \mathrm{{lbf/in^2}}</math>
<!--(1.6**2)/(2*4*pi*10**-7)-->
for the core's saturation limit, <math>B_{sat}</math>. In more intuitive units, it is useful to remember that at 1&nbsp;T the magnetic pressure is approximately {{Convert|4|atm|kg/cm2}}.

Given a core geometry, the magnetic field needed for a given force can be calculated from ({{EquationNote|Eq. 2}}); if the result is much more than 1.6&nbsp;T, a larger core must be used. 

However, computing the magnetic field and force exerted by ferromagnetic materials in general is difficult for two reasons. First, the strength of the field varies from point to point in a complicated way, particularly outside the core and in air gaps, where ''fringing fields'' and ''[[leakage flux]]'' must be considered. Second, the magnetic field and force are [[Nonlinear system|nonlinear]] functions of the current, depending on the nonlinear relation between <math>B</math> and <math>\mathbf{H}</math> for the particular core material used. For precise calculations, computer programs that can produce a model of the magnetic field using the [[finite element method]] are employed.