Ampere's Law

(noun)

An equation that relates magnetic fields to electric currents that produce them. Using Ampere's law, one can determine the magnetic field associated with a given current or current associated with a given magnetic field, providing there is no time changing electric field present.

Related Terms

Examples of Ampere's Law in the following topics:

  • Ampere's Law: Magnetic Field Due to a Long Straight Wire

    • Current running through a wire will produce a magnetic field that can be calculated using the Biot-Savart Law.
    • For a closed curve of length C, magnetic field (B) is related to current (IC) as in Ampere's Law, stated mathematically as:
    • This can be related to the Biot-Savart law.
    • For a short, straight length of conductor (typically a wire) this law generally calculates partial magnetic field (dB) as a function of current for an infinitesimally small segment of wire (dl) at a point r distance away from the conductor:

  • Maxwell's Equations

    • The first two, Gauss's law and Gauss's law for magnetism, describe how fields emanate from charges and magnets respectively.
    • The other two, Faraday's law and Ampere's law with Maxwell's correction, describe how induced electric and magnetic fields circulate around their respective sources.
    • The differential form of Gauss's law for magnetic for magnetism is
    • Ampere's law originally stated that magnetic field could be created by electrical current.
    • The microscopic approach to the Maxwell-corrected Ampere's law relates magnetic field (B) to current density (J, or current per unit cross sectional area) and the time-partial derivative of electric field (E):

  • Electric Currents and Magnetic Fields

    • The Biot-Savart law is written in its complete form as:
    • A more fundamental law than the Biot-Savart law is Ampere's Law, which relates magnetic field and current in a general way.
    • In SI units, the integral form of the original Ampere's circuital law is a line integral of the magnetic field around some closed curve C (arbitrary but must be closed).
    • Ampere's law is always valid for steady currents and can be used to calculate the B-field for certain highly symmetric situations such as an infinite wire or an infinite solenoid.
    • Ampere's Law is also a component of Maxwell's Equations.

  • Maxwell's Equations

    • Proceeding left to right then top to bottom we have Gauss's law, a law without a name, Ampere's law and Faraday's law.
    • It might be more appropriate to call the penultimate, Maxwell's equation, because Ampere's law as it was originally formulated was
    • If one takes the divergence of the complete Ampere's law one obtains,

  • Gauss's Law

    • It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.
    • Gauss's law can be used to derive Coulomb's law, and vice versa.
    • In fact, Gauss's law does hold for moving charges, and in this respect Gauss's law is more general than Coulomb's law.
    • Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.
    • In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.

  • Geomagnetism

    • A magnetic field is generated by a feedback loop: Current loops generate magnetic fields (Ampère's law); a changing magnetic field generates an electric field (Faraday's law); and the electric and magnetic fields exert a force on the charges that are flowing in currents (the Lorentz force).

  • Energy Stored in a Magnetic Field

    • (Eq. 1), where L is the inductance in units of Henry and I is the current in units of Ampere.

  • A Microscopic View: Drift Speed

    • It has units of Amperes per square meter.

  • Overview of Electric Current

    • The SI unit for current is the ampere (A), named for the French physicist André-Marie Ampère (1775–1836).

  • A Review of the Zeroth Law

    • Zeroth law justifies the use of thermodynamic temperature, defined as the shared temperature of three designated systems at equilibrium.
    • This law was postulated in the 1930s, after the first and second laws of thermodynamics had been developed and named.
    • It is called the "zeroth" law because it comes logically before the first and second laws (discussed in Atoms on the 1st and 2nd laws).
    • A brief introduction to the zeroth and 1st laws of thermodynamics as well as PV diagrams for students.
    • Discuss how the Zeroth Law of Thermodynamics justifies the use of thermodynamic temperature