Question

The picture below shows an incomplete pictorial representation of the situation described in this problem. For symmetry reasons, the coordinate system is chosen so that its origin coincides with the point P at which you want to calculate the magnetic field, and the wire lies in the xy plane. The z axis is perpendicular to the page, pointing out of to the page.

As outlined in the strategy above, the wire has been divided into very short segments. For clarity, only one of these segments, segment k of length Δx, is shown in the diagram. In what direction is the magnetic field \(\vec{B}_{\mathrm{k}}\) at P due to segment k alone?

Part B

What can be said about the relative direction of the contributions due to the entire segments KL, LM, and MN to \(\vec{B}_{\mathrm{net}}\) at point \(\mathrm{P}\) ?

•  The magnetic fields due to KL and MN have the same direction; the magnetic field due to LM has the opposite direction. 

•  The three magnetic fields have different directions.

•  All three magnetic fields have the same direction.

Answer 1

According to Biot-Savart law,

From the above figure, we can observe and  for all the three cases. Using the right hand rule, cross product of  ×  (which gives the direction of magnetic field) is in to the plane of figure in all the three cases. Hence all the three magnetic fields have the same direction.