Difference between streamlines of $\vec{E}$ electric field E and electric field lines of $\vec{E}$?

Question

I don't understand how streamlines are related to electric fields. I thought they are related to the lines of fluids.

I searched and saw that streamlines represent curves of velocity vectors, whereas electric fields lines represent curves of electric field vectors.

So I'm confused, what's the difference?

But in our electrostatics course, they asked us to get the streamline equations of $\vec{E}$ (electric field). Do they mean to get the equations of the electric field lines a.k.a. "streamlines"?

Because the way I reasoned this, is the definition of streamlines, is the field lines that are tangent to the velocity vector of the fluid, and here in electrostatics, the electric field vectors are tangent to the electric field lines, so that must mean that electric field lines — streamlines right?

Answer 1

The mathematical relations between the "field lines" of the electric field $\vec{E}(\vec{r})$ and the "streamlines" of the fluid velocity field $\vec{v}(\vec{r})$ are exactly the same. They just sometimes have different names, partly for historical reasons. However, if somebody refers to the "streamlines" of the electric field, they mean the same thing as the electric field lines.

In either case, the direction of the field is always tangent to the direction of the lines. To get the electric field lines from the electric field (which is a vector $\vec{E}$ at each point in space $\vec{r}$), you connect up the arrows representing $\vec{E}$ on the left, to make the continuous lines on the right.

The separation between neighboring lines describes the magnitude $\left|\vec{E}\right|$ of the field. When the lines are farther apart, the field is weaker. For the single charge shown above, the field goes down as $\propto r^{-2}$.

Similarly, here are the streamlines of fluid flowing around a solid sphere.

They are called "streamlines," simply because they describe the streaming of fluid in motion. The direction of the fluid flow is tangent to the lines at each point, and again, the density of the lines is proportional to the speed $|\vec{v}|$. As the flow is deflected around the sphere, the lines get closer together, indicating that the fluid is moving faster.