Exploring the Biot-Savart Law: Is it Determined Experimentally?

In summary, the Biot-Savart Law is similar to Coulomb's Law but for magnetism instead of electricity. Just like Coulomb's Law, there is no mathematical proof for why it exists and it was determined experimentally. However, both laws are necessary for consistency in understanding electricity and magnetism. Maxwell also derived that changing electric fields induce a magnetic field, and there is a derivation of the law of magnetism using only Coulomb's Law and special relativity.
  • #1
amcavoy
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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.
 
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  • #2
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.
 
  • #3
Actually, there is a derivation of law of magnetism using only Coloumb's law and special relativity. See Classical Electrodynamics - Griffiths, 12.3.
 

1. What is the Biot-Savart Law?

The Biot-Savart Law is a fundamental law in electromagnetism that describes the magnetic field produced by a steady current in a conductor. It states that the magnetic field at a point is directly proportional to the current, the length of the conductor, and the sine of the angle between the current and the distance vector from the point to the conductor.

2. How is the Biot-Savart Law determined experimentally?

The Biot-Savart Law can be determined experimentally by measuring the magnetic field at different points around a current-carrying conductor and using those measurements to calculate the constant of proportionality. This process is often done using a device called a Hall probe, which can accurately measure the strength and direction of a magnetic field.

3. Can the Biot-Savart Law be applied to all types of currents?

The Biot-Savart Law is applicable to steady currents, which are those that do not change over time. However, it can also be used to calculate the magnetic field produced by a time-varying electric current, as long as the changes in current are slow enough that the magnetic field can be considered constant at any given point.

4. What are some real-world applications of the Biot-Savart Law?

The Biot-Savart Law has many practical applications, such as in the design of electromagnets, electric motors, and generators. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI) and in the study of the Earth's magnetic field.

5. Are there any limitations to the Biot-Savart Law?

While the Biot-Savart Law is a useful tool for calculating magnetic fields, it does have its limitations. It is only accurate for thin, straight conductors and does not take into account the effects of other nearby conductors or magnetic materials. In some cases, more complex equations, such as the Ampere's Law, may need to be used to accurately calculate the magnetic field.

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