In the figure shown SEGMENT of a straight wire carrying current I is lying along Y-axis. There is a point ‘ P ’ where magnetic field due to this wire is to be calculated.



For the sake of convenience we CHOOSE the FOOT of perpendicular from P to the current carrying wire as origin.

Idl→ is a current element at a distance l from O. Let point P lie in x-y PLANE and r→ is the position vector of point ‘ P ‘ with respect to Idl→ . From figure r→= Ri^ − lj^ . Here i^ and j^ have usual meanings.

Magnetic field at point P due to the current element Idl-> is



Here dB→ is directed along negative Z-axis. The directions of at point P for all elements are same.



This is the general expression for the magnetic field due to straight current.

Now we discuss the different cases.

Case I:

If the wire extends to infinity on either side of ‘ O ‘ then

θ1 = θ2 = π/2 and hence



Case II:

If length of the wire is finite say ‘ L ‘ and P lies on right bisector of wire, then θ1 = θ2 = θ



In this way we can find magnetic field at any point due to straight current.