359,500
V
179,750
V
179,750
V
7,190,000
N/C
1,797,500
N/C
0.3595
J
0.17975
J
-0.17975
J
359,500
V
179,750
V
179,750
V
7,190,000
N/C
1,797,500
N/C
0.3595
J
0.17975
J
-0.17975
J
The Electric Potential Calculator computes the electric potential (voltage) at specified distances from a point charge and the potential difference between two points. Electric potential, denoted V, is a scalar quantity that represents the electric potential energy per unit charge at a given location in an electric field. Defined mathematically as $$V = k\frac{q}{r}$$, the potential provides a powerful alternative to working directly with the electric field vector. Because potential is a scalar, calculating the total potential from multiple charges involves simple arithmetic addition rather than vector addition. The concept of potential difference (voltage) is central to circuit theory, electrochemistry, and virtually all electrical engineering applications. This calculator finds the potential at two distances from a point charge and computes the potential difference and work required to move a unit charge between those points.
The electric potential due to a point charge at distance r is:
$$V = k\frac{q}{r} = \frac{q}{4\pi\varepsilon_0 r}$$
where:
The potential difference between two points at distances r₁ and r₂ is:
$$\Delta V = V_1 - V_2 = kq\left(\frac{1}{r_1} - \frac{1}{r_2}\right)$$
The work done by the electric field in moving a unit positive charge from point 1 to point 2 is $$W = -\Delta V = V_2 - V_1$$. The potential is taken as zero at infinity. Unlike the electric field, potential does not depend on direction — it is the same at all points equidistant from the charge, forming equipotential surfaces (concentric spheres for a point charge). Equipotential surfaces are always perpendicular to electric field lines.
A positive charge creates positive potential that decreases with distance, while a negative charge creates negative potential that increases (becomes less negative) with distance. The potential difference between two points tells you how much energy per coulomb is gained or lost when a charge moves between them. A positive potential difference (V₁ > V₂) means a positive charge naturally moves from r₁ to r₂ (toward lower potential), and the field does positive work. The work per unit charge output gives the external work needed to move a positive charge from r₁ to r₂ against or with the field. In circuits, potential difference is what drives current through resistors and components.
Inputs
Results
A +2 μC charge creates a potential of 359,500 V at 5 cm and 179,750 V at 10 cm. The potential difference of 179,750 V means significant energy is available between these two points. Moving a +1 C charge from 5 cm to 10 cm releases 179,750 J of energy.
Inputs
Results
A −3 μC charge creates negative potentials at both distances. The potential at 2 cm (−1,348,125 V) is more negative than at 50 cm (−53,925 V). A positive test charge would need external work of 1,294,200 J/C to be moved from the farther to the closer point against the attractive field.
Electric potential (V) at a point is the work done per unit positive charge to bring a small test charge from infinity to that point against the electric field. It is a scalar quantity measured in volts (V), where 1 volt = 1 joule per coulomb. The potential is zero at infinity by convention. For a point charge, V = kq/r.
Electric potential (V) is a property of the field at a point in space, measured in volts (J/C). Electric potential energy (U) is the energy of a specific charge placed in that field, measured in joules: U = qV. Potential is energy per unit charge, while potential energy depends on the actual charge being considered.
Potential is defined as work (energy) per unit charge — both work and energy are scalar quantities. The electric field is defined as force per unit charge, and force is a vector. Mathematically, the potential is related to the field by a gradient: E = −∇V. Working with the scalar potential is often simpler because you can add potentials from multiple charges arithmetically without worrying about directions.
Equipotential surfaces are surfaces on which the electric potential has the same value everywhere. For a point charge, they are concentric spheres. No work is done in moving a charge along an equipotential surface. Equipotential surfaces are always perpendicular to electric field lines. The closer together the equipotential surfaces, the stronger the electric field in that region.
The voltage across a circuit element is exactly the electric potential difference between its terminals. A battery maintains a fixed potential difference (EMF) between its terminals, driving current through the circuit. Ohm's Law (V = IR) relates this potential difference to current and resistance. The potential difference is what does work on charges as they flow through the circuit.
Yes. A negative charge creates negative potential at all points in space (V = kq/r with q < 0). Negative potential means that a positive test charge would release energy (do negative work) when brought from infinity to that point — it is naturally attracted. The sign of the potential carries important physical information about the nature of the source charge and the energy landscape.
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