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Field of a solenoid
Intermediate
Uniform inside a long coil.
B = μ₀nIInside a long solenoid B = μ₀nI (n turns per metre), uniform, with nearly zero field outside. Adding an iron core multiplies B by relative permeability.
1000 turns/m at 5 A: 6.3 mT.
Uniform only in the middle of a long coil.
In more detail
A long solenoid carrying current produces a nearly uniform field inside, B = μ0nI, where n is the number of turns per unit length. The field outside is weak.
Real-world uses
- Electromagnets and relays use solenoids to produce fields.
- MRI scanners use long solenoids for uniform fields.
- Magnetic resonance and laboratory instruments use solenoids to create a uniform field inside the coil.
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Frequently asked questions
Why is the field uniform inside?
Because the fields of individual turns add in the middle and cancel near the ends.
What raises the field?
More turns per metre, more current, or a core of soft iron.
Why is a solenoid's field uniform inside?
The fields of the many turns add together along the axis, giving a nearly constant field in the middle of a long coil.
Related topics in Magnetism & Induction
Field of a long straight wire · Field at centre of a loop · Field on axis of a coil · Toroid · Ampere's law · Helmholtz coils