Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 32

32 Figure 29-44a shows an element of length \( ds = 1.00 \text{ mm} \) in a very long straight wire carrying current. The current in that element sets up a differential magnetic field \( d\vec{B} \) at points in the surrounding space. Figure 29-44b gives the magnitude \( dB \) of the field for points 3.5 cm from the element, as a function of angle \( \theta \) between the wire and a straight line to the point. The vertical scale is set by \( dB_s = 120 \text{ pT} \). What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 3.5 cm from the wire?