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Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?

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- Thread starter tade
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In summary, the Biot-Savart and Ampere's Law are equivalent and require that all fields are time-independent and that the stationary current obeys the continuity equation. This can be applied to Faraday's Law, but it is more efficient to use Jefimenko's equation. These laws also have applications in aerodynamics for calculating velocity induced by vortex lines.

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Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?

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http://th.physik.uni-frankfurt.de/~hees/publ/ampere-law-discussion-ver2.pdf

http://dx.doi.org/10.1088/0143-0807/35/5/058001

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vanhees71 said:

http://th.physik.uni-frankfurt.de/~hees/publ/ampere-law-discussion-ver2.pdf

http://dx.doi.org/10.1088/0143-0807/35/5/058001

thanks. I wanted to apply this to Faraday's Law since it also follows Stokes' theorem.

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The Biot-Savart Law is a mathematical equation that describes the magnetic field generated by a steady current, such as a current-carrying wire. It states that the magnetic field at a point is directly proportional to the current, the length of the current-carrying wire, and the sine of the angle between the wire and the point.

The Biot-Savart Law is applicable when the current is steady, the medium is a vacuum or air, and the distances involved are much larger than the dimensions of the current-carrying wire. Additionally, the wire must be thin and straight, and the magnetic field must be weak.

Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. The Biot-Savart Law is a special case of Ampere's Law when the loop is infinitesimal and the current is constant.

No, the Biot-Savart Law is only applicable to steady currents. Permanent magnets have a constantly changing magnetic field, so the Biot-Savart Law cannot be used to calculate their magnetic field.

The Biot-Savart Law is used in various practical applications, such as in the design of electromagnets, motors, and generators. It is also used in medical imaging, such as MRI machines, to create a magnetic field strong enough to produce images of the body's internal structures.

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