# How electric field lines are defined?

I am having confusion understanding that how for finitely many fields lines in the space, the intensity of a field is proportional to the number of field lines passing through a surface area?

Also, suppose that you have a blank sheet of paper and on that there are two point positive charges A and B. How do you draw the field lines? Do you draw some radial rays from A and some from B (with random angles between them, i.e the angular spacing between the radial lines is not same) and then extend each of the rays under the condition that the slope is the direction of electric force? But then how the above condition holds? What of there are many more than just two charges?

"[…]how for finitely many fields lines in the space, the intensity of a field is proportional to the number of field lines passing through a surface area?"

If we draw n equally spaced radial lines outwards from a point positive charge, the number per unit area crossing a spherical surface of radius r centred on the charge will be $\frac{n}{4\pi r^2}$, so will correctly represent the inverse square law of field intensity. We can show that the same thing holds for the field due to more than one static charge.

"[…] there are two point positive charges A and B. How do you draw the field lines? Do you draw some radial rays from A and some from B (with random angles between them"

Why random angles? Close to the either charge itself the field will be radial and symmetrical (if the charge is stationary), so distribute the lines equally all round.

"[…]and then extend each of the rays under the condition that the slope is the direction of electric force?"

That's right. The definition of an electric field line is a line whose direction at each point along it is the direction of the electric field vector at that point. With more than one point charge you have to find the vector sum of their fields at each point, in order to know the direction in which to continue the line. For most purposes you can get away with a rough assessment of the vector sum - quite good practice!

How many lines should you draw? Just enough for the purpose – which is usually to get a rough picture of how the field varies in magnitude and direction around a collection of charges.

• One should note that the lines /unit area is proportional to the field strength only on a sketch in three dimensions. Aug 13 '21 at 14:52
• Good point. And my 3-dimensional sketching isn't that brilliant... Aug 13 '21 at 15:56