Conceptual: field lines never cross. Two point charges of the same sign produce an electric field whose lines never cross and curve sharply between the two charges. Explain why the lines don't cross and what the curvature in the region between the charges represents.
Solution
Why they don’t cross. At every point in space the electric field has a unique direction, determined by the vector sum (superposition principle) of the contributions of all the charges. A field line is by definition tangent to : if two lines crossed, at the crossing point the field would have two different directions at once, which is impossible. So exactly one line passes through each point, and lines cannot intersect.
The curvature between the two charges. In the central region the two contributions, coming from charges of the same sign, point in nearly opposite directions and partially cancel. There is a saddle point (on the axis, at the midpoint) where the field is zero. The lines, repelled by both charges, do not cross this region but skirt around it, bending outward: the curvature precisely visualises this mutual repulsion and the weak field at the centre. Two charges of opposite sign, by contrast, would have lines passing from one to the other, filling the intermediate region.
Links
Topics: Electric field and potential Concepts: Electric field · Electric potential Skills: Superposition principle Methods: Gradient method Objects: Charged sphere