A linear set of wires is given to you. The current in the wires is flowing perpendicular to the plane of paper and towards the reader. The set is infinitely long and the current flowing through the set is uniform and that is lambda amperes per unit width.We have to find out the magnetic field due to this current distribution.
We'll solve this problem by using Ampere's circuital law.
Since, current distribution is uniform, w can create a closed surface for any amount of width.
So, ABCD is the rectangular ampere's closed surface which has a width x. We'll do the calculation with respect to this closed surface. In the diagram, I have shown you the direction of magnetic field B. I found the direction using Fleming's Right Hand Rule. According to this rule, we have to place the thumb along the direction of current, then we have to open our palm and make a pushing movement. The direction along which the palm seems to knock will be the direction of magnetic field.
Now we are going to apply the Ampere's Circuital Law.
In 2 cases, B and dl are parallel to each other. So angle between them is 0 deg. Therefore cos 0 = 1.
In the other 2 cases, B and dl are perpendicular to each other. So angle between them is 90 deg. cos 90 = 0.
Therefore, out of the 4 results, 2 of them are not considered as they are equal to 0.