Problem-solving strategies:
symmetry of electric field and electrostatic potential
near two point charges

This diagram depicts a point p on the line joining two point charges of opposite sign. The problem associated with the diagram might be to solve for the magnitude and direction of the net electric field at point p, or the magnitude and sign of the net electrostatic potential.

Before you attempt to solve such a problem, you should try to predict the qualitative outcome based on consideration of symmetry. The variables to consider are: position of point p relative to the point halfway between the charges, the relative magnitudes of the charges, and the signs on the charges.

The direction of the net electric field at point p turns out to be independent of the magnitudes of the charges and also independent of whether or not p is halfway between the charges. The electric field due to a positive point charge always points away from the charge (to the right when on the right side of it) and the electric field near a negative point charge always points inward toward the charge (to the right when on its left side). So the independent electric fields point in the same direction (to the right).

If you move point p either to the left of Q1 or to the right of Q2, the situation is quite different: at these positions the electric fields due to the individual charges point in opposite directions. The direction of the net electric field will then depend on which charge is strongest and/or closest. Remember that because of Coulomb's Law E ~ 1/r2, and a charge that is twice as far away has to have four times the charge magnitude to have the same influence.
If you make the signs on the two charges the same, the situation is the reverse of what was just described. The fields are opposed in the region between so the net field direction depends on relative charge strength and distance. On either side, the fields point in the same direction and so the net field points away from the pair.

   
If you consider electrostatic potential instead of electric field, all of the arguments above are changed. If the two charges are of opposite sign, the net potential is a difference between numbers anywhere near the two charges in the diagram; between and off to either side. A positive or negative net depends on which charge dominates.

If the two charges are of the same sign, the net potential will always be a sum of two numbers with the sign on the sum being the same as the sign on the charges.

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