Walker, Halliday & Resnick — Magnetic Fields Due to Currents: Problem 62

Figure 29-65 shows, in cross section, four thin wires that are parallel, straight, and very long. They carry identical currents in the directions indicated. Initially all four wires are at distance $d = 15.0 \text{ cm}$ from the origin of the coordinate system, where they create a net magnetic field $\vec{B}$. (a) To what value of $x$ must you move wire 1 along the $x$ axis in order to rotate $\vec{B}$ counterclockwise by $50^{\circ}$? (b) With wire 1 in that new position, to what value of $x$ must you move wire 3 along the $x$ axis to rotate $\vec{B}$ by $30^{\circ}$ back to its initial orientation?