Biot-Savart Law

amcavoy

I read that the Biot-Savart Law is analogous to Coulomb's Law, but for Magnetism instead of Electricity. Back when we learned about Coulomb's Law, I remember my professor saying that Coulomb's law cannot be explained and that there is no mathematical proof for why Coulomb's Law exists. Is this the same for the Biot-Savart Law? Was it determined experimentally?

Thanks in advance.

lightgrav

There's no "proof" that one mass must attract all other masses
. . . but they DO - we describe it by saying that
being surrounded by a Gravitational field is one characteristic of mass.

There's no "proof" that there "has to be" a property like charge,
which is surrounded by an electric field as one of its characteristics.
. . . but there IS - so we describe it in a similar manner.

Because the Magnetic field is "produced" by charge in motion,
it is NOT autonomous from the E-field that is already described.
You will soon be shown a way to obtain a Magnetic field contribution
that is "induced" by a *change* in the E-field.
But NO one would have thought of that without having first treated
the moving charge as the source.

Electricity and Magnetism are tightly related - like Potential and Kinetic E -
and we can prove things about one, if given the other.

If we know "everything there is to know" about Electric fields, we could
derive that Biot-Savart was needed in order to be consistent.
If we know "everything there is to know" about Magnetic fields, we could
probably show that Coulomb was needed to be consistent.

Historically, Coulomb and Biot-Savart were verified by experiment,
and Maxwell derived that changing E-fields must induce a B-field.

gulsen

Actually, there is a derivation of law of magnetism using only Coloumb's law and special relativity. See Classical Electrodynamics - Griffiths, 12.3.