This online Electric Potential Calculator finds the potential at a point in space created by an arbitrary system of point electric charges. You just need to specify the magnitude of the charges and their distance to the point of measurement of the electric potential. To add or delete a charge you may click the “+” symbol or the “–” symbol respectively.
What is Electric Potential
Electric potential is a scalar quantity that describes the electric potential energy per unit charge at a specific point in space. In simpler terms, it tells us how much electric potential energy a unit positive charge would have at that point. Electric potential is measured in volts (V), and it is a crucial concept in understanding the behavior of electric fields and the movement of charged particles.
Electric potential is analogous to gravitational potential energy, which tells us how much potential energy an object has due to its position in a gravitational field. Similarly, electric potential is a measure of how much potential energy a charged particle possesses due to its position in an electric field.
The Electric Potential Formula
The electric potential at a point in space can be calculated using the following formula, which is easy to derive using Coulomb’s law:
$$V = k_{e} \cdot \frac{q}{r},$$
where
• \(V\) is the electric potential at the point (in volts, V),
• \(q\) is the magnitude of the point charge creating the electric potential (in coulombs, C),
• \(r\) is the distance from the point charge to the point where the potential is being calculated (in meters, m),
• \(k_{e}\) is the Coulomb’s constant, its value is approximately equal to 8.98755 × 10⁹ N·m²/C².
This formula illustrates that the electric potential is directly proportional to the magnitude of the charge creating it and inversely proportional to the distance from that charge. In other words, as the magnitude of the charge increases, the electric potential also increases, while increasing the distance decreases the electric potential.
Electric Potential of a System of Point Charges
Now, let’s explore how to calculate the electric potential at a point in space created by a system of multiple point charges. It is quite obvious that the electric potential at a point due to a system of point charges is the sum of the electric potentials created by each individual charge.
Mathematically, for a system of point charges \(q_1\), \(q_2\), … \(q_n\) located at positions \(r_1\), \(r_2\), … \(r_n\) in space, the electric potential at a point \(P\) is given by:
$$V = k_{e} \sum_{i=1}^{n} \frac{q_i}{r_i},$$
where
• \(V\) is the electric potential at point \(P\),
• \(q_i\) is the magnitude of the \(i\)-th point charge,
• \(r_i\) is the distance from the \(i\)-th point charge to point \(P\),
• \(k_{e}\) is the Coulomb’s constant.
The summation symbol represents the sum of the electric potentials created by all individual point charges.
This formula emphasizes that the electric potential at a point in space due to multiple point charges is the algebraic sum of the potentials created by each individual charge. Each term in the summation accounts for the contribution of one point charge to the total electric potential.
Electric Charge and Electric Charge Units
Electric charge is a fundamental property of matter that describes the imbalance of positive and negative particles within an object. It is the basis for the existence of electric fields and electric forces.
Charged particles can be either positively or negatively charged, and objects can possess a net charge if the number of positive or negative charges is uneven. Like charges repel each other, while opposite charges attract.
Electric сharge has dimension T·I. The SI unit of electric сharge is coulomb (C). In physics and chemistry the elementary charge (e) is commonly used as a unit. In electrical engineering it is also used the ampere-hour (A⋅h).
When using our Electric Potential Calculator, you can easily choose any unit of measurement that is convenient for you.
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