Equations 22-8 and 22-9 are approximations of the magnitude of the electric fiel

Question

Equations 22-8 and 22-9 are approximations of the magnitude of the electric field of an electric dipole, at points along the dipole axis. Consider a point P on that axis at distance z = 9.00d from the dipole center(where d is the separation distance between the particles of the dipole). Let Eappr be the magnitude of the field at point P as approximated by Equations 22-8 and 22-9. Let Eact be the actual magnitude. By how much is the ratio Eappr/Eact less than 1?

Thanks, I really can't get this one but I know im close to the answer.

Explanation / Answer

Let us put d = 2l; z = 8.00 d = 16.00 l; l/z = 1/16 E' = E approx = k2p/z3----(1) E = Eactual = k2p.z/(z2 -l2)2-----(2) E'/E = (z2-l2)2/z4 = (1 -l2/z2)2 = 1 -2x(1/16)2 + --- = 1 - 2x0.00391 Therefore, 1 - E'/E = 0.00782 (E -E')/E = 0.00782 = 0.782% Thus, the ratio, Eapprox/Eactual is less than 1 by0.00782

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