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Maxwellkid
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how is the Biot Savart law derived?? From where does it come?
The Biot Savart Law is an equation that describes the relationship between a magnetic field and the current that produces it. It is named after French physicist Jean-Baptiste Biot and French mathematician Félix Savart.
The formula for the Biot Savart Law is B = (μ₀/4π) * (I * dl x ̂r)/r², where B is the magnetic field, μ₀ is the permeability of free space, I is the current, dl is the infinitesimal length of the current element, r is the distance between the current element and the point where the magnetic field is being measured, and x ̂r is the unit vector pointing from the current element to the point where the magnetic field is being measured.
The units of the Biot Savart Law are teslas (T) for the magnetic field, amperes (A) for the current, meters (m) for the length of the current element, and meters (m) for the distance between the current element and the point where the magnetic field is being measured.
The Biot Savart Law is an important equation in electromagnetism, as it allows us to calculate the magnetic field produced by a current-carrying wire or a series of current-carrying wires. It is also used in the study of magnetic fields and their effects on charged particles.
The Biot Savart Law can be derived from Ampere's Law and the principle of superposition. It involves integrating the magnetic field contributions from each infinitesimal current element along the path of the current. This derivation requires knowledge of vector calculus and is often covered in advanced electromagnetism courses.