Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 4

4 Equation 29-4 gives the magnitude \( B \) of the magnetic field set up by a current in an infinitely long straight wire, at a point \( P \) at perpendicular distance \( R \) from the wire. Suppose that point \( P \) is actually at perpendicular distance \( R \) from the midpoint of a wire with a finite length \( L \). Using Eq. 29-4 to calculate \( B \) then results in a certain percentage error. What value must the ratio \( L/R \) exceed if the percentage error is to be less than 3.00%? That is, what \( L/R \) gives \[ \frac{(B \text{ from Eq. 29-4}) - (B \text{ actual})}{(B \text{ actual})} (100\%) = 3.00\%? \]