Two equal electric currents are flowing perpendicular to each other as shown in the figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the currents. Where do we expect the resultant magnetic field to be zero?

Question

Accepted Answer

(2) On AB. Given: one wire along +y and one along +x, carrying equal currents; AB is the diagonal through the first and third quadrants, CD the one through the second and fourth. Idea: at any point, each wire makes a field perpendicular to the page, so the two either add or cancel depending on their signs. Vertical wire (current up): at a point with x>0 its field is into the page; with x<0, out of the page. Horizontal wire (current right): at a point with y>0 its field is out of the page; with y<0, into the page. On AB, where y=x: in the first quadrant one is into the page and the other out, and the distances from the two wires are equal, so the magnitudes match and they cancel. The same holds in the third quadrant. On CD, where y=-x: both are out of the page in the second quadrant and both into it in the fourth, so they add. The resultant field is zero on AB.

Two equal electric currents are flowing perpendicular to each other as shown in the figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the currents. Where do we expect the resultant magnetic field to be zero?

Step-by-step solution

Why the other options are wrong