Why does the potential go to infinity (white) right on top of a charge?

The formula for potential from a point charge is V = kq/r. As the distance r approaches zero, the value of V becomes infinitely large. This is a limitation of the point charge model—in reality, charges have finite size, so the potential at their center remains large but finite. The simulator shows this singularity to correctly represent the mathematical model.

How are the electric field and electric potential related in this simulator?

The electric field is the negative gradient of the electric potential (E = -∇V). This means the electric field points in the direction of steepest decrease in potential and is always perpendicular to the equipotential lines. While this simulator visualizes potential, you can infer the field: it points from high potential (red) to low potential (blue) and is strongest where the equipotential lines are closest together.

Can this simulator model a capacitor or a conductor?

Not directly. A capacitor requires two extended, oppositely charged conductors, which create a uniform potential gradient. This simulator uses only point charges. For a conductor, the entire surface must be an equipotential, which would require a complex rearrangement of charge on its surface—a dynamic process not modeled here. This tool is best for understanding the fundamental potential from discrete, fixed point charges.

What do the units on the potential color scale represent?

The units are volts (V), which are joules per coulomb (J/C). The scale is relative and auto-scales based on the charges present. A value of +10 V at a point means a +1 C test charge placed there would have 10 J of electric potential energy. The key takeaway is the pattern and relative values, not the absolute numbers, unless you define specific charge magnitudes and distances.

Electric Potential

Electric potential is a scalar field that describes the potential energy per unit charge at any point in space due to a distribution of source charges. This simulator visualizes this fundamental concept by calculating and displaying the net electric potential V at every point in a two-dimensional plane using the principle of superposition: V = Σ (k q_i / r_i). Here, k is Coulomb's constant (8.99 × 10^9 N·m²/C²), q_i is the value of each point charge, and r_i is the distance from that charge to the point of calculation. The resulting potential is shown as a continuous color heatmap, where colors represent different voltage levels, and distinct lines trace equipotential contours—paths where the potential is constant. Users can drag positive and negative point charges to instantly see how the potential landscape deforms, observing how like charges create potential 'hills' or 'ridges' and opposite charges create a 'valley' or 'saddle' between them. The model simplifies reality by restricting the view to 2D, treating charges as dimensionless points, and ignoring any dielectric or conductive materials that would distort the field. It also assumes a static configuration, with no moving charges or magnetic effects. By interacting, students directly explore the scalar nature of potential, contrast it with the vector electric field, understand the additive property of potential, and see the geometric relationship between equipotential lines and field direction (they are always perpendicular).

Who it's for: High school and introductory university physics students studying electrostatics, as well as educators seeking a dynamic tool to illustrate electric potential and superposition.

Key terms

Electric Potential
Equipotential Line
Point Charge
Superposition Principle
Coulomb's Constant
Scalar Field
Voltage
Electrostatics

How it works

Scalar electric potential from point charges: V = Σ k qᵢ / r (same plane, relative units). The heatmap uses blue for lower V and red for higher V. Near each charge the magnitude blows up — color limits are set from the rest of the plane so you can still see structure. E⃗ = −∇V, so field lines run downhill on this map for a positive test charge.

Key equations

V(r⃗) = Σ k qᵢ / |r⃗ − r⃗ᵢ| · E⃗ = −∇V

Frequently asked questions

Why does the potential go to infinity (white) right on top of a charge?: The formula for potential from a point charge is V = kq/r. As the distance r approaches zero, the value of V becomes infinitely large. This is a limitation of the point charge model—in reality, charges have finite size, so the potential at their center remains large but finite. The simulator shows this singularity to correctly represent the mathematical model.
How are the electric field and electric potential related in this simulator?: The electric field is the negative gradient of the electric potential (E = -∇V). This means the electric field points in the direction of steepest decrease in potential and is always perpendicular to the equipotential lines. While this simulator visualizes potential, you can infer the field: it points from high potential (red) to low potential (blue) and is strongest where the equipotential lines are closest together.
Can this simulator model a capacitor or a conductor?: Not directly. A capacitor requires two extended, oppositely charged conductors, which create a uniform potential gradient. This simulator uses only point charges. For a conductor, the entire surface must be an equipotential, which would require a complex rearrangement of charge on its surface—a dynamic process not modeled here. This tool is best for understanding the fundamental potential from discrete, fixed point charges.
What do the units on the potential color scale represent?: The units are volts (V), which are joules per coulomb (J/C). The scale is relative and auto-scales based on the charges present. A value of +10 V at a point means a +1 C test charge placed there would have 10 J of electric potential energy. The key takeaway is the pattern and relative values, not the absolute numbers, unless you define specific charge magnitudes and distances.

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