Question

Draw electric field lines and equipotential surfaces for a system of two equal and opposite point charges separated by some distance.

Hint:

When sketching diagrams manually in exams, strictly guarantee that every single intersection point between an equipotential dashed line and a solid electric field line visually appears completely perpendicular (a perfect $90^\circ$ cross).

Answer 1

Concept:
• A structural system purely comprising two equal and entirely opposite point charges rigorously separated by a tiny distance is officially termed an electric dipole.
• Electric field lines organically originate strictly from the positive charge and terminate cleanly on the negative charge, smoothly curving through surrounding space.
• Equipotential surfaces inherently represent 3D geometric surfaces where the total electrical potential remains completely constant. They must always rigidly intersect electric field lines at perfect $90^\circ$ right angles.

Step 1: Describe the Electric Field Lines
\includegraphics[width=0.5\linewidth]{25i_sol.png}
Draw a distinct positive charge ($+q$) securely on the left and a negative charge ($-q$) securely on the right.
Draw continuous, smooth curves confidently leaving the positive charge and securely entering the negative charge.
The field lines strictly along the direct axis connecting them travel straight across. The lines above and below actively bow outward gracefully.
Ensure that absolutely no two field lines ever physically cross each other, and indicate the proper direction strictly with arrows pointing precisely towards the negative charge.

Step 2: Describe the Equipotential Surfaces
Since the electric potential of a dipole is $V = \frac{1}{4\pi\epsilon_0} \left( \frac{q}{r_1} - \frac{q}{r_2} \right)$, the absolute central point exactly midway between the charges strictly has zero potential.
Draw a large, flat vertical plane perfectly bisecting the central distance between the charges. This central equatorial plane is exactly a $0\text{V}$ equipotential surface.
Closer to the charges, carefully draw dashed or dotted circular curves closely encircling each individual charge.
These encircling surfaces must visually bunch up closer together aggressively within the central region between the two charges where the field is distinctly stronger, and dynamically spread further apart on the extreme outer sides.