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Ampere's law
Intermediate
Line integral of B equals μ₀ times enclosed current.
∮B·dl = μ₀I∮B·dl = μ₀I_enc: like Gauss's law for magnetism, it gives fields with symmetry easily. Maxwell added displacement current.
Straight wire: B·2πr = μ₀I.
Choose an amperian loop that exploits symmetry.
In more detail
Ampère's law states that the line integral of the magnetic field around a closed loop equals μ0 times the enclosed current. It is a powerful tool for symmetric current distributions.
Real-world uses
- Engineers use Ampère's law to design long wires and solenoids.
- It is the magnetic analogue of Gauss's law.
- Engineers use Ampère's law to find the magnetic field of long wires and solenoids with high symmetry.
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Frequently asked questions
What counts as enclosed current?
Currents passing through a surface bounded by the loop, with signs given by the right-hand rule.
Does it need symmetry?
It is most useful with symmetry, but it is generally true for steady currents.
When is Ampère's law easy to use?
When the field is constant along a chosen closed path, such as a circle around a long wire.
Related topics in Magnetism & Induction
Field on axis of a coil · Field of a solenoid · Toroid · Helmholtz coils · Magnetic dipole moment · Magnetic materials