The magnetic field of a straight wire line

Example I The Magnetic Field of a Straight Wire Line 

Consider a current I flowing through a vertical line as shown in Fig. 1.28. We will define the magnetic field at an arbitrary point, a, in a cylindrical system of coordinates, r, 0, z with the z-axis along the current-carrying line. 

Starting with Biot-Savart law, we can say that the magnetic field has axial symmetry and is represented by a single component From the principle of superposition, one can say that the total field is the sum of a number of fields contributed by current elements / dz. Then we have  

Let / be the angle between the current element dz and a vector that extends from this element to the observation point. It should be clear that we have  

Let us suppose that the current-carrying line is infinitely long, so that two angles a and 02 take the values tt/2 and —7t/2, respectively. Then  

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