Question

Part A

Two charges, +q and -q, are located in the x-y plane at points (0,+d/2) and (0,-d/2), respectively. Calculate the magnitude of the electric field at point P with the superposition principle.

Data: q = 13.0 nC, d = 4.40 mm and P is at x = 88.0 mm.

Part B

In the previous problem, you can get an approximate answer for the electric field at point P by using the electric dipole approximation which is valid for the limit x>>d. Calculate the magnitude of the electric field at point P with this approximation and the same values for Q, d and x as in the previous problem.

Answer 1

Exact: At P, each E vector has equal/opposite x component and equal/same y component = kq/r^2*sin(theta) = kq/r^2*(d/2)/r = kqd/(2r^3)

E(total) = kqd/r^3

k = 9*10^9

q = 13*10^-9 C

r^3 = (0.0022^2+0.088^2)^1.5=6.82*10^-4

E(total) = 9*10^9*13*10^-9*0.0044/6.82*10^-4 = 754.83 V/m

b. Approx.: E = kqd/x^3 = 9*10^9*13*10^-9*0.0044/0.088^3 = 755.4 V/m

The difference is due to the fact that the approximation uses x in place of r.