Your boss is designing a new data storage system that will have a lot of dipoles very close to one another. They will point in the \(z\) direction and be closely spaced in the \(x\) and \(y\) directions. The data reader will detect \(E_{z}\) as it passes some small distance above the sheet of dipoles. You know that Equation 23. 13 is valid only for large distances from the dipole, but it is much easier to apply than the exact result. You prefer the easiest calculation possible, but your boss demands \(1.00 \%\) accuracy at distances only a few dipole separations from one of the source dipoles.

Data from Equation 23. 13

E = k[(1+2)-(1-2)] Ey 2y, 9 2d = k- 9pd = 2k- = 2k- P (yd/2).