Calculate Electrical Potential From A Positive and Negative Charge

Electrical potential is the work needed to move a unit positive charge from one point to another in an electric field. This calculator helps you determine the potential difference between two charges using Coulomb's Law, which relates the force between two charges to the distance between them.

How to Calculate Electrical Potential

To calculate the electrical potential between two charges, you'll need to know:

The magnitude of the first charge (q₁)
The magnitude of the second charge (q₂)
The distance between the two charges (r)

The calculation involves determining the force between the charges and then converting that force to potential energy. The result is expressed in volts (V).

Note: This calculation assumes the charges are point charges and the medium is a vacuum. For real-world scenarios, you may need to account for the dielectric constant of the medium.

Coulomb's Law Formula

The electrical potential (V) between two charges can be calculated using Coulomb's Law:

V = k × (q₁ × q₂) / r

Where:

V = electrical potential (volts)
k = Coulomb's constant (8.9875 × 10⁹ N·m²/C²)
q₁ = magnitude of first charge (coulombs)
q₂ = magnitude of second charge (coulombs)
r = distance between charges (meters)

The formula shows that potential increases with larger charges and decreases with greater distances between them.

Worked Example

Let's calculate the potential between two charges:

Charge 1 (q₁) = 2 × 10⁻⁶ C
Charge 2 (q₂) = -3 × 10⁻⁶ C
Distance (r) = 0.1 m

Using the formula:

V = (8.9875 × 10⁹) × (2 × 10⁻⁶ × -3 × 10⁻⁶) / 0.1

V = (8.9875 × 10⁹) × (-6 × 10⁻¹²) / 0.1

V = -5.3925 × 10⁻² V

The negative sign indicates that the potential is higher at the negative charge than at the positive charge. The absolute value of -0.053925 V represents the potential difference between the two points.

Interpreting the Result

The calculated potential difference tells you:

How much work is needed to move a charge between the two points
The relative strength of the electric field between the charges
The direction of the electric field (from positive to negative)

In practical applications, this information helps in designing circuits, understanding electrostatic interactions, and analyzing the behavior of charged particles in electric fields.

FAQ

What units should I use for the charges and distance?

For consistency, use coulombs (C) for charges and meters (m) for distance. The calculator will handle the conversion automatically.

Can I calculate potential for charges of the same sign?

Yes, but the result will be positive, indicating a repulsive force between the charges.

What if the charges are not point charges?

The formula assumes point charges. For extended charge distributions, you would need to integrate over the charge distribution.

How does the potential change with distance?

The potential decreases inversely with distance, following the 1/r relationship in Coulomb's Law.