Calculate the Electric Field (E) and Electric Potential (V) at a point due to a point charge.
Understanding Electric Field and Electric Potential
This calculator helps determine two fundamental properties of electrostatics: the Electric Field (E) and the Electric Potential (V) created by a point charge at a specific distance.
The Physics
When an electric charge exists, it creates an electric field in the space around it. This field exerts a force on any other charge placed within it. The electric field strength at a point is defined as the force per unit charge experienced by a test charge at that point. For a point charge q, the magnitude of the electric field E at a distance r is given by Coulomb's Law:
E = k * |q| / r^2
Where:
E is the electric field strength in Newtons per Coulomb (N/C).
k is Coulomb's constant, approximately 8.98755 × 10^9 N⋅m²/C².
|q| is the magnitude of the point charge in Coulombs (C).
r is the distance from the point charge to the point where the field is being measured, in meters (m).
The electric field is a vector quantity, meaning it has both magnitude and direction. The direction of the electric field is radially outward from a positive charge and radially inward towards a negative charge. This calculator provides the magnitude.
The electric potential (also known as voltage) represents the amount of electric potential energy per unit charge at a point in an electric field. It's the work done per unit charge to move a test charge from infinity to that point against the electric field. For a point charge q, the electric potential V at a distance r is given by:
V = k * q / r
Where:
V is the electric potential in Volts (V).
k is Coulomb's constant (8.98755 × 10^9 N⋅m²/C²).
q is the point charge in Coulombs (C). Note that the sign of the charge affects the sign of the potential.
r is the distance from the point charge, in meters (m).
Use Cases
Understanding electric fields and potentials is crucial in many areas of physics and engineering, including:
Designing electronic components and circuits.
Analyzing the behavior of charged particles in accelerators.
Studying electromagnetic waves and radiation.
Investigating phenomena like lightning and static electricity.
Modeling the interactions of atoms and molecules.
Example Calculation
Let's calculate the Electric Field and Electric Potential due to a charge of +2.0 × 10^-9 C at a distance of 0.5 meters.
V = (8.98755 × 10^9 N⋅m²/C²) * (2.0 × 10^-9 C) / (0.5 m)
V = (8.98755 × 10^9) * 2.0e-9 / 0.5
V ≈ 35.95 V
The calculator will output these values for you to verify.
function calculateEO() {
var charge = parseFloat(document.getElementById("charge").value);
var distance = parseFloat(document.getElementById("distance").value);
var k = 8.98755e9; // Coulomb's constant in N m^2 / C^2
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(charge) || isNaN(distance)) {
resultDiv.innerHTML = "Please enter valid numbers for charge and distance.";
return;
}
if (distance <= 0) {
resultDiv.innerHTML = "Distance must be a positive value.";
return;
}
// Calculate Electric Field Magnitude
var electricField = k * Math.abs(charge) / (distance * distance);
// Calculate Electric Potential
var electricPotential = k * charge / distance;
var resultHTML = "Electric Field (E): " + electricField.toFixed(2) + " N/C";
resultHTML += "Electric Potential (V): " + electricPotential.toFixed(2) + " V";
resultDiv.innerHTML = resultHTML;
}