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##### Chapter 27 Sources of Magnetic Field

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**Topics**• The Biot-Savart Law • Gauss’s Law for Magnetism • Ampere’s Law**The Biot-Savart Law**A point charge produces an electric field. When the charge moves it produces a magnetic field, B: m0 is the magnetic constant: As drawn, the field is into the page**The Biot-Savart Law**Example: Compute field at point P, due to particle moving along z axis**The Biot-Savart Law**Example:**The Biot-Savart Law**When the expression for B is extended to a current element, Idl, we get the Biot-Savart law: The magnetic field at a given point P1 is the sum of the field from each element**P**Biot-Savart Law: InfinitelyLong Straight Wire The magnetic field due to an infinitely long current-carrying wire can be computed from the Biot-Savart law. The magnitude of the magnetic field is:**Force Between Conductors**Recall that the force on a current-carrying wire in a magnetic field is Therefore, two parallel wires, with currents I1 and I2 exert a magnetic force on each other. The force on wire 2 is:**Magnetic Flux**Just as we did for electric fields, we can define, for a magnetic field, a flux in a similar way: But there is a profound difference between the two kinds of flux…**Gauss’s Law for Magnetism**Isolated positive and negative electric charges exist. However, no one has ever found an isolated magnetic north or south pole, that is, no one has ever found a magnetic monopole Consequently, for any closed surface the magnetic flux into the surface is exactly equal to the flux out of the surface**Gauss’s Law for Magnetism**This yields Gauss’s law for magnetism Unfortunately, however, because this law does not relate the magnetic field to its source it is not useful for computing magnetic fields. But there is a law that is…**I**Ampere’s Law If one sums the dot product around a closed loop that encircles a steady current I then Ampere’s law holds: That law can be used to compute magnetic fields, given a problem with sufficient symmetry