Biot-Savart’s law
The source of the steady magnetic field may be a permanent magnet, an electric field changing linearly with time, or a direct current. We shall largely ignore the permanent magnet and save the time-varying electric field for a later discussion. Our present relationships will concern the magnetic field produced by a differential dc element in free space.
Biot-Savart’s law states that the magnetic field intensity dH produced at a point P as shown in figure by the differential current element is proportional to the product Idl and the sine of the angle α.
AMPERE’S CIRCUIT LAW
After solving a number of simple electrostatic problems with Coulomb’s law, we found that the same problems could be solved much more easily by using Gauss’s law whenever a high degree of symmetry was present. Again, an analogous procedure exists in magnetic fields. Here, the law that helps us to solve problems more easily is known as Ampere’s circuital law, sometimes called Ampere’s work law.
Amper circuit law states that the line integral of H around a closed path is exactly the same as the current Ienc enclosed by the path.
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