Biot-Savart: Why symmetry-break?

Thread starter geonat
Start date Dec 14, 2008
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Biot-savart

In summary: Yes, the magnetic field is a convention, and there is a simpler alternative that would produce the same results.

Jan 7, 2009

Phrak

turin said:

If I'm not mistaken, magnetic monopoles and EM gauge invaraince cannot be simulaneously true, or at least a magnetic monopole introduces some weird topological branch in space, but I guess this wouldn't be so catastrophic if they always came in pairs.

Defining the electric and magnetic fields as spacetime derivatives of a potential field precludes magnetic monopole fields on a simply connected manifold. (All closed forms are exact.) Something about deRham cohomology. This is probably what you've heard, but it's not true. I've disproved it--though I cheated. I get a low energy regime where everything looks normal with one kind of charge. Higher energies allow monopole fields.

Last edited: Jan 7, 2009

<h2>1. What is the Biot-Savart Law?</h2><p>The Biot-Savart Law is a fundamental law in electromagnetism that describes the magnetic field produced by a steady current in a wire. It states that the magnetic field at a point is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the point.</p><h2>2. How does the Biot-Savart Law relate to symmetry-breaking?</h2><p>The Biot-Savart Law is used to calculate the magnetic field produced by a current in a wire. In cases where there is symmetry in the current distribution, the resulting magnetic field will also exhibit symmetry. However, when the current distribution is not symmetrical, the resulting magnetic field will also not be symmetrical, hence the term "symmetry-breaking."</p><h2>3. Why is symmetry-breaking important in the study of electromagnetism?</h2><p>Symmetry-breaking is important because it allows us to understand and predict the behavior of magnetic fields in non-symmetrical situations. This is crucial in many practical applications, such as designing electromagnets and understanding the behavior of magnetic fields in complex systems.</p><h2>4. Can the Biot-Savart Law be applied to all current distributions?</h2><p>No, the Biot-Savart Law is only applicable to steady current distributions. In cases where the current is changing over time, other laws such as Ampere's Law or Faraday's Law must be used.</p><h2>5. How is the Biot-Savart Law derived?</h2><p>The Biot-Savart Law is derived from the fundamental equations of electromagnetism, such as Maxwell's equations and the Lorentz force law. It can also be derived using vector calculus and the principle of superposition.</p>

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 wire. It states that the magnetic field at a point is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the point.

2. How does the Biot-Savart Law relate to symmetry-breaking?

The Biot-Savart Law is used to calculate the magnetic field produced by a current in a wire. In cases where there is symmetry in the current distribution, the resulting magnetic field will also exhibit symmetry. However, when the current distribution is not symmetrical, the resulting magnetic field will also not be symmetrical, hence the term "symmetry-breaking."

3. Why is symmetry-breaking important in the study of electromagnetism?

Symmetry-breaking is important because it allows us to understand and predict the behavior of magnetic fields in non-symmetrical situations. This is crucial in many practical applications, such as designing electromagnets and understanding the behavior of magnetic fields in complex systems.

4. Can the Biot-Savart Law be applied to all current distributions?

No, the Biot-Savart Law is only applicable to steady current distributions. In cases where the current is changing over time, other laws such as Ampere's Law or Faraday's Law must be used.

5. How is the Biot-Savart Law derived?

The Biot-Savart Law is derived from the fundamental equations of electromagnetism, such as Maxwell's equations and the Lorentz force law. It can also be derived using vector calculus and the principle of superposition.