SolenoidA long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet. Such coils, called solenoids, have an enormous number of practical applications. The field can be greatly strengthened by the addition of an iron core. Such cores are typical in electromagnets.
In the above expression, n is the number of turns per unit length, sometimes called the "turns density". The expression is an idealization to an infinite length solenoid, but provides a good approximation to the field of a long solenoid.

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Solenoid Field from Ampere's LawTaking a rectangular path about which to evaluate Ampere's Law such that the length of the side parallel to the solenoid field is L gives a contribution BL inside the coil. The field is essentially perpendicular to the sides of the path, giving negligible contribution. If the end is taken so far from the coil that the field is negligible, then the length inside the coil is the dominant contribution.

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Solenoid Magnetic Field Calculation
The Earth's magnetic field is about half a gauss. The relative permeability of magnetic iron is around 200. Enter data, then click on the quantity you wish to calculate in the active formula above the data entry points. Default values will be entered for unspecified parameters, but the numbers will not be forced to be consistent until you click on the quantity to calculate.

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