Biot-Savart Law: Proven or Guessed?

[Bobhawke]

Is the Biot Savart law similar to the coulomb law in that it is something that is guessed initially, and later shown to give the same solution that Maxwell's equations give (except Maxwell's equations are a generalisation), or is it something that is proven? And if it is proven, could someone provide that proof.

Thanks

 

[Meir Achuz]

Physical laws are based on experimental observation.
The B-S law was deduced by Laplace, based on measurements by Biot and Savart.
Maxwell later derived one of his equations from it.
You can derive Max's equation from B-S or B-S from Max's equation, so they are connected, but the proof is in the pudding (experiment).

 

[charng]

for your question. The Biot-Savart law is a fundamental law in electromagnetism, which describes the magnetic field produced by a current-carrying wire. It is similar to the Coulomb's law in that it is a mathematical equation that was initially derived from experimental observations and later shown to be consistent with Maxwell's equations. However, unlike the Coulomb's law, the Biot-Savart law cannot be derived from first principles. It is considered a "postulate" in electromagnetism.

The Biot-Savart law is based on the experimental observations of Jean-Baptiste Biot and Felix Savart in the early 19th century. They found that the magnetic field produced by a current-carrying wire is directly proportional to the current, the length of the wire, and inversely proportional to the distance from the wire. This led to the mathematical form of the Biot-Savart law, which has been verified by numerous experiments.

While the Biot-Savart law cannot be derived from first principles, it is considered a "proven" law in electromagnetism. This means that it has been extensively tested and found to accurately describe the behavior of magnetic fields produced by current-carrying wires. In fact, the Biot-Savart law is a key component of many important applications, such as electromagnets, motors, and generators.

In terms of mathematical proof, the Biot-Savart law can be derived from Maxwell's equations, which are a set of four fundamental equations that describe all of electromagnetism. However, this derivation requires a deep understanding of vector calculus and is beyond the scope of this response.

In conclusion, the Biot-Savart law is a proven law in electromagnetism, based on experimental observations and consistent with Maxwell's equations. While it cannot be derived from first principles, it has been extensively tested and is a crucial tool in understanding and using magnetic fields in various applications.