Example l. Calculate the magnetic flux density of an infinitelylonglinecurrentofl.Solution: Select the cylindrical coordinatesystem, and let the line current be along the z.axis, then the direction of the vector dl x(r -r')dlis that of B. And the direction of the crossproduct vector is that of the unit vector es, andthe direction of B is that of es, i.e.B= Beawhich states that the magneticfield lines are a set of the circles withthe center at the z-axis,and the magneticflux densitiesisindependentof the variable o.Sincethe line currentisinfinitelylong,the fields musthave nodependence on z.u
Example 1. Calculate the magnetic flux density of an infinitely long line current of I. r O z y x dl I r ′ r – r ′ e Solution: Select the cylindrical coordinate system, and let the line current be along the zaxis, then the directionof the vector is that of B. And the direction of the cross product vector is that of the unit vector e , and the direction of B is that of e , i.e. dl (r − r) B = Be which states that the magnetic field lines are a set of the circles with the center at the z-axis, and the magnetic flux densities is independent of the variable . Since the line current is infinitely long, the fields must have no dependence on z
In this case, the circulation of the magnetic flux density around themagneticfield lineof radius risB·dl = B2元 rBased on Ampere's circuitallaw, we haveμo1B=2元rWe can prove that this equation is valid forBthe magnetic fields outside the cylindricalconducting wire of certain cross section andcarrying a current I.UV
In this case, the circulation of the magnetic flux density around the magnetic field line of radius r is d = B2π r B l Based on Ampere’s circuitallaw, we have r I B 2π 0 = We can prove that this equation is valid for the magnetic fields outside the cylindrical conducting wire of certain cross section and carrying a current I. I B