Trouble with Biot-Savart Law: Instant Effects & Ampere-Maxwell Law

In summary, the Biot-Savart Law applies in magnetostatics with constant currents, while Coulomb's Law applies in electrostatics with constant charge densities. Both are specific cases of the Jeffimenko equations, which describe the electric and magnetic fields from changing charges.
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LeoPedranjo
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Guys, I'm having trouble with some concepts on the Biot-Savart Law. Lots of texts compare this law with Coulomb Law, but doesn't affirm that B-S is only applicable on a static case (constant current). What are the real physical conditions in which Biot-Savart Law can be directly applied? Does it covers the instant eletromagnetic effects with the distance (as the Coulomb Law doesn't)?
Also, to surpass the instant effects over distance, could I aplly the Ampere-Maxwell law?

Thanks!
 
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Long story short, The Biot-savart law applies in magnetostatics, where currents are constant in time.
Similarly, Coulomb's law, applies in electrostatics, where charge densities are constant in time (though individual charges may be moving)

These laws are special cases of what are known as the Jeffimenko equations, which completely describe the electric and magnetic field generated from an arbitrarily changing collection of charges (both Wikipedia and Griffith's E&M book have good introductions).
 
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FAQ: Trouble with Biot-Savart Law: Instant Effects & Ampere-Maxwell Law

What is the Biot-Savart Law?

The Biot-Savart Law is a fundamental law in electromagnetism that describes the magnetic field produced by a current-carrying wire. It states that the magnetic field at a given point is directly proportional to the current, length, and sin of the angle between the wire and the point.

What are the instant effects of the Biot-Savart Law?

The Biot-Savart Law describes the instantaneous magnetic field at a given point, without taking into account the time it takes for the field to propagate. This means that the effects of the law are felt immediately at the given point, without any delay.

What is the Ampere-Maxwell Law?

The Ampere-Maxwell Law is another fundamental law in electromagnetism that describes the relationship between electric currents and changing electric fields. It states that the circulation of the electric field around a closed loop is equal to the rate of change of the magnetic flux through the loop.

What is the relationship between the Biot-Savart Law and the Ampere-Maxwell Law?

The Biot-Savart Law and the Ampere-Maxwell Law are closely related and are both necessary for a complete understanding of electromagnetism. The Biot-Savart Law describes the magnetic field produced by a current, while the Ampere-Maxwell Law describes the relationship between changing electric fields and magnetic fields.

What are some practical applications of the Biot-Savart Law and the Ampere-Maxwell Law?

The Biot-Savart Law and the Ampere-Maxwell Law have many practical applications, including in the design of electric motors, generators, and transformers. They are also used in medical imaging techniques such as MRI, as well as in the study of Earth's magnetic field and the behavior of charged particles in space.

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