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A tangent from a point can be extended in either direction at a time, so how do we determine the direction of electric field at that point?

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    $\begingroup$ Welcome to the site. It's quite difficult to answer this question as written without a diagram or some more precise words of explanation of exactly what you're asking, I can't really follow what you mean by "tangent from a point" here. $\endgroup$
    – catalogue_number
    Oct 6, 2021 at 0:39

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By convention, the direction of the electric field at any point is the direction of the force that a positive charge would experience if placed at that point.

Hope this helps.

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According to Wikipedia:

A field line is a graphical visual aid for visualizing vector fields. It consists of a directed line which is tangent to the field vector at each point along its length. A diagram showing a representative set of neighboring field lines is a common way of depicting a vector field in scientific and mathematical literature; this is called a field line diagram. They are used to show electric fields, magnetic fields, and gravitational fields among many other types. In fluid mechanics field lines showing the velocity field of a fluid flow are called streamlines.

  • In usual practice, only finite number of field lines are drawn.

  • The way to draw obeys some rules. For example, the line density (therefore flux density) is proportional the field strength.

  • Illustration of Gauss' Law (2D or 3D): For a selected a closed contour (or surface in $3$D), number of outward lines minus the number of inward lines is proportional to the net charge enclosed.

enter image description here

  • Field line pattern gives a qualitative visualization only. Only direction (with arrows shown or polarities known) of the vector field (but no magnitude) for an arbitray point on a selected field line is known.

  • For a point not on the field lines drawn, we need to guess the direction (usually more or less parallel to adjacent field lines) when the exact mathematical expression of the vector field is not known.

  • Alternatively, we can use CAS to plot vector fields on regular lattice points such as Wolfram Alpha:

enter image description here

See also mathematical treatment of electric field pattern in my post here.

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  • $\begingroup$ You haven't told the OP what determines the direction of the arrow of the field line, which I think was the question $\endgroup$
    – Bob D
    Oct 6, 2021 at 14:42
  • $\begingroup$ OP mentioned tangent, we can guess at least field line pattern is known. But if only the field pattern is given without showing arrows and knowing the polarities of the singularities (sources and sinks), both directions are possible providing Gauss' law still held. Plotting vector field is more concise though looks less elegant. $\endgroup$
    – Ng Chung Tak
    Oct 6, 2021 at 21:18
  • $\begingroup$ Yes, but I have never seen field lines without arrows, in which case, it begs the question as to what determines the direction of the arrows shown, which was the basis of my answer. But I would agree that it is not totally clear what the OP is asking for, thus the reason it has been closed. $\endgroup$
    – Bob D
    Oct 6, 2021 at 21:24
  • $\begingroup$ Please feel free to see my previous post. Due to software limitation, arrows were omitted. Also, the dimension was squeezed to $2$ so that the force law became $\dfrac{1}{r}$ so as the Gauss' Law preserved. $\endgroup$
    – Ng Chung Tak
    Oct 6, 2021 at 23:44

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