Two equal but opposite charges form a dipole. Describe the equipotential surface on which \(V=0\)

The concept of electric potential is fundamental in understanding electric fields and forces. Electric potential at a point in space is defined as the amount of work done in moving a unit positive charge from infinity (where the potential is taken as zero) to that point without acceleration. It's the potential energy per unit charge, measured in volts (V), where one volt is equivalent to one joule per coulomb.

In the case of an electric dipole, which consists of two equal and opposite charges, the electric potential due to each charge can be added algebraically because potential is a scalar quantity. For a dipole, this results in an equation for the potential at any point in space. When this potential equals zero, it indicates that the contributions from both charges cancel each other out at that location. This concept is crucial when determining the equipotential surface where the potential is zero, as in the problem we are examining.

Coulomb's constant (\( k \)) is a proportionality factor that appears in Coulomb's law, which governs the magnitude of the electrostatic force between two point charges. The value of Coulomb's constant is approximately equal to \( 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2} \).

The constant is derived from the equation \( F = k \frac{\left| q_1 \cdot q_2 \right|}{r^2} \), where \( F \) is the force between charges, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between them. Understanding Coulomb’s constant is essential for calculating the electric potential due to a point charge or a system of charges, like a dipole, since it relates the charge and distance to the potential energy within the field.

Equipotential surfaces are imaginary surfaces in an electric field on which the electric potential is the same at every point. No work is required to move a charge along an equipotential surface, as there is no change in potential energy. For different charge configurations, these surfaces can have various shapes, such as spherical for point charges or cylindrical for line charges.

Specifically, for an electric dipole, the equipotential surface where the potential is zero is an infinite plane that bisects the dipole perpendicularly at its midpoint. This is because, at any point on this plane, the distance to the positive and negative charges is the same, so the contributions to the potential due to each charge will cancel out. Visualizing equipotential surfaces provides a deeper understanding of the electric field structure and aids in the analysis of electrical potential distribution around charge configurations.