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Solenoid and Magnets

A 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.

 

Solenoid Field from Ampere's Law

Taking a rectangular path about which to evaluate Ampere's Law such that the length of the side parallel to the solenoic 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.

This admittedly idealized case for Ampere's Law gives

This turns out to be a good approximation for the solenoid field, particularly in the case of an iron core solenoid.

 

Solenoid Magnetic Field Calculation

At the center of a long solenoid
Magnetic field = permeability x turn density x current

 

 

 

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