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Vector potential
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A field A with B = ∇×A.
B = ∇×A defines the vector potential, simplifying electrodynamics; E = −∇V − ∂A/∂t. The Aharonov–Bohm effect shows A has physical effects.
Used in quantum theory.
A isn't uniquely defined (gauge freedom).
In more detail
The magnetic vector potential A is a field whose curl gives the magnetic field, B = ∇ × A. It simplifies calculations of fields and is central to quantum mechanics.
Real-world uses
- Quantum mechanics uses the vector potential to describe charged particles in fields.
- Calculating magnetic fields from current distributions.
- Theoretical physicists use the vector potential to describe magnetic fields in quantum mechanics.
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Frequently asked questions
Is A physically measurable?
Its curl is measurable as B, though A itself is defined up to a gauge choice.
Why is it useful?
It makes some calculations easier, especially in quantum theory.
Is the vector potential measurable?
Not directly, but it affects the phase of quantum particles, as seen in the Aharonov–Bohm effect.
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