An electric potential calculator is a valuable tool for anyone studying physics or electrical engineering. It helps you determine the electric potential energy of a charged particle at a given point in an electric field. Electric potential is a measure of the work done to move a unit charge from a reference point to a specific point in an electric field without any acceleration.

What is Electric Potential?

Electric potential is a measure of the work done per unit charge in bringing a charge from infinity to a specific point in an electric field. It is an essential concept in electrostatics, allowing us to understand how electric charges interact and the energy associated with those interactions.

Formula for Electric Potential

Due to a Point Charge

The electric potential due to a single point charge is given by:

\( V = \frac{q}{4 \pi \varepsilon_0 \varepsilon_r \, r} \)

Where:

• \(V\): Electric potential (Volts)

• \(q\): Charge (Coulombs)

• \(r\): Distance from the charge (Meters)

• \(\varepsilon_0\): Permittivity of free space \((8.854 \times 10^{-12} \, \text{F/m})\)

• \(\varepsilon_r\): Relative permittivity of the medium

Due to a System of Point Charges

If multiple charges are involved, the total potential at a point is the sum of the potentials due to each charge. The formula is:

$$ V = \frac{1}{4 \pi \epsilon_0 \epsilon_r} \left( \frac{q_1}{r_1} + \frac{q_2}{r_2} \right) $$

Where:

• \( V \) = Potential
• \( \epsilon_0 \) = Permittivity of free space
• \( \epsilon_r \) = Relative permittivity
• \( q_1, q_2 \) = Charges
• \( r_1, r_2 \) = Distances from the charges

This formula accounts for multiple point charges, summing their individual potentials to find the overall potential at a given point.

Potential Difference between Two Points

The difference in electric potential between two points 𝐴 and 𝐵 in the field is called the electric potential difference and is calculated as:

$$ V = \frac{1}{4 \pi \epsilon_0 \epsilon_r} \cdot \frac{q}{r} $$

Where:

• \( V \) is the electric potential (in volts, V)
• \( q \) is the charge (in coulombs, C)
• \( r \) is the distance from the charge (in meters, m)
• \( \epsilon_0 = 8.854 \times 10^{-12} \, \text{F/m} \) is the permittivity of free space (a constant)
• \( \epsilon_r \) is the relative permittivity (dimensionless)

This formula helps calculate the voltage difference, which is essential for understanding energy transfer between two points in an electric field.

Explanation of the Formula

The formulas demonstrate how the potential depends on various factors:

• \(\text{Charge } (q): \text{ The greater the charge, the higher the electric potential.}\)

• \(\text{Distance } (r): \text{ As the distance from the charge increases, the potential decreases.}\)

• \(\text{Relative Permittivity } (\varepsilon_r): \text{Higher permittivity lowers electric potential.}\)

• \(\text{System of Charges: The total potential is the sum of the potentials due to individual charges.}\)

• \(\text{Potential Difference: It explains the energy required to move a charge between two points.}\)

Example Calculation

Given:

• \(\text{Charge } (q) = 4 \times 10^{-7} \, C\)

• \(\text{Distance } (r) = 10 \, \text{m}\)

• \(\text{Relative Permittivity } (\varepsilon_r) = 2\)

Solution:

Using the formula:

\(V = \dfrac{1}{4 \pi \times (8.854 \times 10^{-12}) \times 2} \cdot 10 \times (4 \times 10^{-7})\)

After simplifying:

\(V \approx 7.079 \times 10^{3} \, \text{V}\)

The electric potential at a distance of 10 meters from the charge is approximately 7079 volts.

Unit of Electric Potential

The unit of electric potential is the Volt (V). One volt is the potential required to move one coulomb of charge using one joule of energy. This relationship is expressed as:

\(1 \, \text{V} = \dfrac{1 \, \text{C}}{1 \, \text{J}}\)

Where 𝐽 is joules (energy) and 𝐶 is coulombs (charge).

Table of Electric Potential Calculator

Here’s a sample table of gold costs per pound based on various total costs and weights:

Quantity	Symbol	Unit	Unit Symbol
Electric Potential	\(V\)	Volt	V
Electric Charge	\(q\)	Coulomb	C
Distance	\(r\)	Meter	m
Permittivity of Free Space	\(\varepsilon_0\)	Farad per Meter	F/m
Relative Permittivity	\(\varepsilon_r\)	– (Dimensionless)	–

Significance of Electric Potential

Electric potential is essential for:

• Circuit Design: Ensuring proper voltage distribution.

• Energy Transfer: Measuring energy required to move charges.

• Field Analysis: Understanding the behavior of electric fields.

• Battery Efficiency: Monitoring voltage for performance.

• Capacitors: Calculating stored energy.

Functionality of the Electric Potential Calculator

The electric potential calculator simplifies the computation of electric potential for a point charge or multiple charges.

To use the tool:

1. Input the charge (q) in coulombs.
2. Enter the distance (r) in meters.
3. Provide the relative permittivity (ϵᵣ).

The calculator instantly computes the potential in volts. It can also be used as an electric potential energy calculator by combining the results with energy formulas.

FAQs

What is the purpose of an electric potential calculator?

It simplifies the calculation of electric potential at a point due to charges.

How does the electric potential energy calculator differ?

The electric potential energy calculator determines the energy required to move a charge in an electric field, using the formula 𝑈 = 𝑞 ⋅ 𝑉 .

Can the calculator handle multiple charges?

Yes, it calculates the total potential by summing individual potentials.

How does relative permittivity affect the result?

Knowing the gold cost per pound is crucial for bulk purchases, investment strategies, and managing manufacturing costs, ensuring informed financial decisions.