Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 60

60 Two long straight thin wires with current lie against an equally long plastic cylinder, at radius \( R = 20.0 \text{ cm} \) from the cylinder’s central axis. Figure 29-64a shows, in cross section, the cylinder and wire 1 but not wire 2. With wire 2 fixed in place, wire 1 is moved around the cylinder, from angle \( \theta_1 = 0^\circ \) to angle \( \theta_1 = 180^\circ \), through the first and second quadrants of the \( xy \) coordinate system. The net magnetic field \( \vec{B} \) at the center of the cylinder is measured as a function of \( \theta_1 \). Figure 29-64b gives the \( x \) component \( B_x \) of that field as a function of \( \theta_1 \) (the vertical scale is set by \( B_{xs} = 6.0 \text{ \mu T} \)), and Fig. 29-64c gives the \( y \) component \( B_y \) (the vertical scale is set by \( B_{ys} = 4.0 \text{ \mu T} \)). (a) At what angle \( \theta_2 \) is wire 2 located? What are the (b) size and (c) direction (into or out of the page) of the current in wire 1 and the (d) size and (e) direction (into or out of the page) of the current in wire 2?