Field Line Plot

There are two uniform spherical charge distributions, each with radius $1$ . Distribution $1$ is centered at $(x_1, y_1, z_1) = (-2,0,0)$ and has charge $+1$ . Distribution $2$ is centered at $(x_2, y_2, z_2) = (2,0,0)$ and has charge $-1$ . Let us plot the electric field lines in the following manner.

1) Begin at point $(x_0, y_0, z_0) = (x_1 + \cos \theta_0, y_1 + \sin \theta_0, 0)$
2) Update the coordinates as follows:

$x_k = x_{k-1} + \epsilon \, \hat{E}_{x \, k-1} \\ y_k = y_{k-1} + \epsilon \, \hat{E}_{y \, k-1} \\ z_k = 0$

3) Continue plotting until the field line hits the boundary of charge distribution $2$
4) Make plots for the following values of $\theta_0$ , resulting in $25$ field lines: $\pm 120^\circ, \pm 110^\circ, \pm 100^\circ, \pm 90^\circ, \pm 80^\circ, \pm 70^\circ, \pm 60^\circ, \pm 50^\circ, \pm 40^\circ, \pm 30^\circ, \pm 20^\circ, \pm 10^\circ, 0^\circ$

In step $2$ , subscript $k$ denotes the present value, and subscript $(k-1)$ denotes the previous value. $\hat{E}$ is a unit-length version of the net electric field at point $(x,y,z)$ . The parameter $\epsilon$ is a very small number.

What is the combined length of all $25$ field lines?

Details and Assumptions:
1) $\frac{1}{4 \pi \epsilon_0} = 1$
2) To check results, it helps to run the plotter with $\epsilon$ values spanning several orders of magnitude.