The forum discussion centers on calculating magnetic flux density using the Biot-Savart law, specifically addressing the integration of current elements in the x-y plane. Participants critique the initial approach, highlighting the importance of correctly defining the vectors dl and R, which should only have components in the x and y directions, as the problem is confined to the x-y plane. The necessity of multiplying the final result by three to account for three wires is emphasized, along with the need for clarity on the integration limits from -a to a. The discussion underscores the significance of the right-hand rule in determining the direction of the magnetic field.
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You are correct. Neither dl nor R should have components along ez. Since the triangle lies in the x-y plane (z=0), dl should have components along ex and ey. Also, R should only have components along ex and ey because it's pointing from the location of dl , which is in the x-y plane, to the origin, which is also in the x-y plane. Accordingly, the cross product dl x R would come out to be along ez, which is what we should expect from the right hand rule.mfb said: