# Problem in understanding superposition principle in electrostatics

When I have a single charge, it produces a electric field and a test charge will experience a force. Now when I have two(identical,same sign) charges, they produce electric fields and when the test charge is placed it will experience a force which is sum of the forces due to each of the charges according to principle of superposition.

In the 2nd diagram the field lines are perpendicular from both sources and are added. But from superposition principle the field lines are inclined as shown in diagram 3 but direction is same but according to me the magnitude should be different from that of diagram 2. So I am definitely wrong in my intuition as superposition works. I want to know where I am wrong? You just apply the principle of superposition. Your new configuration of field lines for the two charge case will be determined based on the superposition of the fields from each charge individually.

But my problem is when two charges produce fields, the field lines will change(as they interact)their directions.

Field lines don't "interact", unless by interact you just mean the fields add (due to superposition). The new field lines, as said above, will jut be determined based on the superposition of the two individual fields. Field lines are a way we can visualize electric fields, but at the end of the day we just have electric fields. The electric field is just a vector field (i.e. at each point in space you have an associated electric field vector). Since we cannot visualize a drawing of all vectors at all points in space (due to the density of points, or the overlap of the vectors) we draw field lines to get a rough idea of the electric field.

It should be noted that field lines and the vectors are not the same thing.

• Sorry I edited a bit late but the picture added is how I am visualising the interactions. Can u help me to understand where I am wrong? Jun 14 '19 at 16:10
• @TrilokGirishKamagond Your picture looks fine. I don't understand your issue Jun 14 '19 at 16:11
• Again sorry I modified the question now. Jun 14 '19 at 16:18
• @TrilokGirishKamagond I am sorry, I still do not understand. All of your diagrams are correct. You just add the vectors together at each point in space to get the new field configuration. From there you can draw your field line diagrams. You should note that in diagram 2 you are drawing field lines, and in diagram 3 you are drawing vectors. Maybe that is where your confusion lies. Jun 14 '19 at 16:44
• Actually my diagram 3 also shows field lines. I understood from both answers that my diagram 2 is a result of superposition itself. I thought about it differently. Thank you so much for your answers Jun 14 '19 at 16:48

I agree with @Aaron Stevens answer. This will simply elaborate on it by giving examples of electric field lines when multiple charge are involved. See the diagrams below.

When you have two charges in proximity the direction of the electric field at each location is simply the vector sum of the electric field vectors for each individual charge. This is not easy to show so, as Aaron pointed out, we use electric field lines to give us an idea of both the direction of the field using arrows (by convention the direction of the force that a positive charge would experience if placed in the field) as well as the relative strength of the field (indicated by the relative density of the field lines). So the direction of the vector sum is indicated by the direction of the arrows in the diagrams and the relative magnitude of the strength of the vector sum is indicated by the relative density of the field lines.

The two diagrams below are an example for the case of two equal negative charges and two equal positive and negative charges. For two positive charges, simply take the diagram of the two negative charges and change the direction of the field arrows.

Note the relative density of the field lines at different locations. They indicate the relative strength of the field at that location.

Hope this and Aaron’s answer together help. • So in my second diagram the field strength would be less as compared to the 3rd diagram making the magnitudes same? What I understood from your answer is that- it happens because of less field lines at that point in space. Jun 14 '19 at 16:29
• I understood your clear answer thank you so much Jun 14 '19 at 16:49