# Is the relative number of electric field lines between two charges proportional to the difference between those two charges?

Let us consider a system of two unlike charges and suppose that the magnitude of the positive charge is greater that of the negative charge and call them a and b respectively.

If that(asked in the title) is true then if we keep them close together then more field lines will be generated from the a but less field lines will end in charge b. What happens to those field lines that don't end ? We are only considering those field lines that are not away from the system (or those that can actually end

• Hint: What happens to the field lines when you just have one point charge? – The Photon May 2 '19 at 5:42

The number of field lines will be the same.

The electric field lines are pictorial depictions of the electric vector field. The best way to imagine it is to leave a test charge in the field and track its movement. If you perform this mental exercise, you will find that the field lines get denser near the charge with the higher magnitude and are rarer near the on with lower magnitude. This happens since the charge with higher magnitude attracts/repels the test charge with a greater force than the other charge.

What happens to those field lines that don't end ?

The field lines don't end if the charge is isolated. They simply radiate outward or inward. If the charge is not isolated, some of the lines will end at the other opposite charge. Others will not if they are not sufficiently influenced by the other charge.

To illustrate this, the figure below shows the field lines produced by positive and negative charge where the magnitude of the positive charge (call it charge $$a$$) is greater than the negative charge (call it charge $$b$$) as in the example you cite. The arrows point to the path that a positive test charge placed in the field will take. The density of the field lines at any location indicates the relative strength of the field (Newtons per coulomb or volts per meter) at that location.

Notice that some of the field lines of the positive charge end at the negative charge. But most do not because the lower magnitude negative charge has less influence on the field of the positive charge. On the other hand most of the field lines of the negative charge end at the positive charge, because of the greater influence of the positive charge on the field of the negative charge. Even those that don't end at the positive charge are "bent" more due to the influence of the positive charge.

If the charges are far enough apart all the field lines of each would radiate out (for the positive charge) or in (for the negative charge) without ending.

Hope this helps.