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I am curious how you derive this law. It seems that you could derive coulomb ` s law from gauss ` s law, but are there are no similar analogy for Bio-Savart law.
arunbg said:Both Coulomb's law and Biot-Savart's laws were framed from experimental analysis of electomagnetic phenomena. They are fundamental and cannot be "derived" as such. However it can be said that coulomb's law is consistent with gauss's law, and biot-savart's with ampere's circuital law.
stevenb said:However, I'm an engineer, not a mathematician, so I'll just wait until a smart guy shows up to give us the answer.
The Biot-Savart law is an equation that describes the magnetic field generated by a steady electric current. It states that the magnetic field at a certain point is directly proportional to the current at that point and the distance between the point and the current.
The Biot-Savart law can be derived using the principle of superposition and the cross product of two vectors. It also involves integrating over the current distribution to calculate the magnetic field at a specific point.
The Biot-Savart law assumes that the current is steady and that the magnetic field is generated by a single, infinitely thin wire. It also assumes that the distance between the current and the point of interest is much greater than the size of the current-carrying wire.
The Biot-Savart law is used in various fields such as electromagnetism, astrophysics, and engineering. It is used to calculate the magnetic field of different current-carrying systems, such as wires, coils, and solenoids. It is also used in the design and analysis of electric motors, generators, and other electromagnetic devices.
The Biot-Savart law is applicable to steady, direct currents. It cannot be used to calculate the magnetic field of alternating currents, which require a more complex equation known as Ampere's law. However, for low-frequency alternating currents, the Biot-Savart law can still provide a good approximation.