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Given a positive charge the electric field lines are drawn starting from the charge and pointing radially outward, ending in principle at infinity, according to the electric field strength being proportional to the inverse square of distance. From the definition of electric field we know that the modulous of the electric field is greater for smaller distances from the field generating charge. Since the electric field lines point radially outward we consider the density of lines an indication of the strength of the electirc field. If we immagine to trace a circle around the electric field generating charge, of radius slightly greater than the radius of the object which holds the charge and therefore generates the electric field, such circle will be crossed by a number 'n' of lines. The density of lines crossing the cirle will then be the circumference of the circle divided by the number 'n' of lines. For a larger circle we will have a greater circumference, but same number of lines 'n', and therefore a smaller density of lines crossing it, which idicates a lower intesity of electric field for a greater distance from the charge.
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Where do electric field lines point?
The electric field lines are directed away from a positive charge and towards a negative charge so that at any point , the tangent to a field line gives the direction of electric field at that point.
Does field exist between lines?
Yes, usually. The lines are simply shown to illustrate direction and strength of the field.
What are equipotential lines?
A uniform electric field exists between parallel plates of equal but opposite charges.
Why do two magnetic lines never intersect each other?
It is important to realize that magnetic lines do not really exist! They are a tool to visualize the magnetic field, but the field is continuous and does not exist solely inside lines. The direction of the lines gives the direction of the magnetic field, the density of lines, its strength. This also explains why no two field lines can ever intersect; a field line carries information about the direction of the magnetic field, if they would intersect an ambiguity would arise about the direction (not to mention a field of apparent infinite strength since the density would be infinite at the point of crossing). The field lines are almost never used in explicit calculations; instead one uses a vector, an entity which contains information about the magnitude and direction of a field in every point in space and time. Adding two magnetic fields is then easy; just add the vectors of both fields in every point in space (and time). You can use the resulting vector field to draw field lines again if you want. An easy way to imagine what would happen to field lines when they might intersect is to look at them as being such vectors. Imagine you have one field line pointing to the right, and another one pointing up. The result of adding would be a field line pointing somewhere in the up-right direction (the exact direction depending on the relative magnitudes of the fields). If the fields are equal in magnitude but opposite in direction they would cancel; the field line disappears. But this is to be expected! The magnetic fields canceled each other in that point! One has to take care with this analogy however; as for field lines the measure of magnitude is their density; which is an undefined thing if you are considering just one field line per field. For a vector however, the measure of magnitude is its length. Therefore adding two field lines of the same magnitude and pointing in the same direction would result in a vector of twice the length, but in field line language you would have to double the density at that point. This is one of the reasons field lines are used for visualization but not calculation. By the way, all these things apply to other fields as well. Electric fields can also be represented by field lines, and they as well cannot intersect (for the same reasons). Electric field lines, however, are not necessarily closed loops like magnetic field lines (this has to do with the non-existence of magnetic monopoles).
Where do magnetic field lines cross?
Magnetic field lines don't cross.
