Relation between magnetic vector potential and magnetic flux
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term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, or simply vector potential, A; and the magnetic scalar potential ψ. Both quantities can be used in certain circumstances to calculate the magnetic field B.
The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field: curl A = B. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials A and φ. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.
The magnetic scalar potential ψ is sometimes used to specify the magnetic H-field in cases when there are no free currents, in a manner analogous to using the electric potential to determine the electric field in electrostatics. One important use of ψ is to determine the magnetic field due to permanent magnetswhen their magnetization is known. With some care the scalar potential can be extended to include free currents as well.[citation needed]
Historically, Lord Kelvin first introduced vector potential in 1851, along with the formula relating it to the magnetic field
The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field: curl A = B. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials A and φ. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.
The magnetic scalar potential ψ is sometimes used to specify the magnetic H-field in cases when there are no free currents, in a manner analogous to using the electric potential to determine the electric field in electrostatics. One important use of ψ is to determine the magnetic field due to permanent magnetswhen their magnetization is known. With some care the scalar potential can be extended to include free currents as well.[citation needed]
Historically, Lord Kelvin first introduced vector potential in 1851, along with the formula relating it to the magnetic field
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