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Electromagnet
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==Simple solenoid== {{main|Solenoid}} [[File:VFPt Solenoid correct2.svg|thumb|upright=1.5|Magnetic field produced by a [[solenoid]] (coil of wire). This drawing shows a cross-section through the center of the coil. The crosses are wires in which current is moving into the page; the dots are wires in which current is moving up out of the page.]] A common tractive electromagnet is a uniformly wound solenoid and plunger. The solenoid is a coil of wire, and the plunger is made of a material such as soft iron. Applying a current to the solenoid applies a force to the plunger and may make it move. The plunger stops moving when the forces upon it are balanced. For example, the forces are balanced when the plunger is centered in the solenoid. The maximum uniform pull happens when one end of the plunger is at the middle of the solenoid. An approximation for the force {{mvar|F}} is<ref name="Marks 105"/> {{Numblk|:|<math>F = \frac{C A N I}{\ell}</math>|{{EquationRef|1}}}} where {{mvar|C}} is a proportionality constant, {{mvar|A}} is the cross-sectional area of the plunger, {{mvar|N}} is the [[number of turns]] in the solenoid, {{mvar|I}} is the current through the solenoid wire, and {{mvar|β}} is the length of the solenoid. For long, slender, solenoids (in units using inches, pounds force, and amperes), the value of {{mvar|C}} is around 0.009 to 0.010 psi (maximum pull pounds per square inch of plunger cross-sectional area).<ref name="Marks 105-6">{{harvnb|Dawes|1967|loc=p. 15-105β15-106}}</ref> For example, a 12-inch-long coil ({{math|1=''β'' = 12 in}}) with a long plunger with a cross section of one inch square ({{math|1=''A'' = 1 in<sup>2</sup>}}) and 11,200 [[ampere-turn]]s ({{math|1=''N I'' = 11,200 Aturn}}) had a maximum pull of 8.75 pounds (corresponding to {{math|1=''C'' = 0.0094 psi}}).<ref>{{harvnb|Dawes|1967|loc=p. 15-106, Table 25}}</ref> The maximum pull is increased when a magnetic stop is inserted into the solenoid. The stop becomes a magnet that will attract the plunger; it adds little to the solenoid pull when the plunger is far away but dramatically increases the pull when the plunger is close. An approximation for the pull {{mvar|P}} is<ref name="auto">{{harvnb|Dawes|1967|loc=p. 15-106}}</ref> :<math>P = A N I \left[\frac{N I}{(\ell_\mathrm{a})^2 (C_1)^2} + \frac C \ell\right] = \frac{A N^2 I^2}{(\ell_\mathrm{a})^2 (C_1)^2} + \frac{C A N I}{\ell}</math> Here {{math|''β''<sub>a</sub>}} is the distance between the end of the stop and the end of the plunger. The additional constant {{math|''C''<sub>1</sub>}} for units of inches, pounds, and amperes with slender solenoids is about 2660<!-- units? -->. The first term inside the bracket represents the attraction between the stop and the plunger; the second term represents the same force as the solenoid without a stop ({{EquationNote|1|Eq. 1}}). Some improvements can be made on this basic design. The ends of the stop and plunger are often conical. For example, the plunger may have a pointed end that fits into a matching recess in the stop. The shape makes the solenoid's pull more uniform as a function of separation. Another improvement is to add a magnetic return path around the outside of the solenoid (an "iron-clad solenoid").<ref name="auto" /><ref>{{cite book |last=Underhill |first=Charles R. |date=1906 |title=The Electromagnet |publisher=D. Van Nostrand |page=113 |url=https://books.google.com/books?id=n9tYAAAAYAAJ&pg=PA113 |url-status=live |archive-url=https://web.archive.org/web/20160501182508/https://books.google.com/books?id=n9tYAAAAYAAJ&pg=PA113&lpg=PA113&hl=en&f=false |archive-date=2016-05-01 }}</ref> The magnetic return path, just as the stop, has little impact until the air gap is small.
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