Question

The equation Upper E equals StartFraction 1 Over 2 pi epsilon Subscript 0 EndFraction StartFraction q ⁢ d Over z Superscript 3 EndFraction is approximation 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 = 23.00d from the dipole center (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 the equations below. Let Eact be the actual magnitude. What is the ratio Eappr /Eact?

Answer 1

E_aprox = 1.003 E_real

Step-by-step explanation:

In this exercise we are given the expression for the electric field of a dipole in the axis direction of the dipole

E_real = k 2q d / √(z² + d²)³

I think your equation has some errors.

In this case they indicate that d is the separation of the charges of the dipole

in the case of z »d this equations approximates

E_aprox = k 2q d/ z³

calculate the value for the two cases

E_real = k2q d / √[ ((23d)² + d²)³]

E_real = k2q d / d³ 12201

E_real = k2q 1/12201 d²

E_aprox = k2q d / (23.00d)³

E_aprox = k2q 1/12167 d²

the error between these quantities is

E_aprox / E_real = 12201 d² / 12167 d²

E_aprox / E_real = 1.003

E_aprox = 1.003 E_real