Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

THe answer is not 0.5 or 0.5x10^-4 or .25 The equation E = 1/2 pi epsilon_0 q0\'

ID: 1536721 • Letter: T

Question

THe answer is not 0.5 or 0.5x10^-4 or .25

The equation E = 1/2 pi epsilon_0 q0'/z^3 is approximation of the magnitude of the electric field of an electric dipole, at points along the dipole axis. Consider a point rho on that axis at distance z = 22.00dfrom the dipole center (d is the separation distance between the particles of the dipole). Let E_appr be the magnitude of the field at point rho as approximated by the equations below. Let E_act be the actual magnitude. What is the ratio E_appr/E_act?

Explanation / Answer


Eappr = (1/(2*pi*eo))*(q*d/z^3)

1/(4*pi*eo) = 9*10^9

1/(2*pi*e0) = 2*9*10^9 = 18*10^9

Eappr = (18*10^9)*(q*d/(22*d)^3 = (18*10^9)*q*/(484*d^2)

Eact = (1/(2*pi*eo))*(q*d*z)/(z^2-d^2)^2

Eact = (18*10^9*q*d*22*d)/(22^2d^2-d^2)^2

Eact = 18*10^9*22*q*d^2 /(483^2*d^4) = 18*10^9*22*q/(233289*d^2)

Eappr /Eact = (1/484)/(22/483^2) = 21.9