Lecture

Ampère-Laplace Law: Magnetic Field Calculation and Applications

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In course

PHYS-201(d): General physics : electromagnetism

The topics covered by the course are concepts of electromagnetism, properties of waves, and fluid mechanics. ...

Description

This lecture covers the derivation and application of the Ampère-Laplace law (or Biot-Savart law) for calculating the magnitude and direction of magnetic fields generated by currents. It explains how to apply the law to different wire configurations, perform integrations, and evaluate magnetic fields around straight wires and current loops. The integral forms of the law for wire sections and surface currents are discussed, along with practical examples like determining the magnetic field of a rectilinear wire and a current loop. The lecture concludes with considerations on calculating magnetic field strength along the central axis of a loop.

Instructor

Dirk Grundler

Official source

Ontological neighbourhood

Physics

Electromagnetism: Electrodynamics

Related concepts (31)

Ampère's circuital law

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamics in his 1861 published paper "" In 1865 he generalized the equation to apply to time-varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law, which is one of Maxwell's equations which form the basis of classical electromagnetism.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.

Earth's magnetic field

Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic field is generated by electric currents due to the motion of convection currents of a mixture of molten iron and nickel in Earth's outer core: these convection currents are caused by heat escaping from the core, a natural process called a geodynamo.

Interplanetary magnetic field

The interplanetary magnetic field (IMF), now more commonly referred to as the heliospheric magnetic field (HMF), is the component of the solar magnetic field that is dragged out from the solar corona by the solar wind flow to fill the Solar System. The coronal and solar wind plasmas are highly electrically conductive, meaning the magnetic field lines and the plasma flows are effectively "frozen" together and the magnetic field cannot diffuse through the plasma on time scales of interest.

Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: . 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 φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.

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