Calculate electric field strength E = k·q / (εᵣ·r²), electric potential V = k·q / (εᵣ·r), force on a charge F = q·E, distance, and charged particle kinematics in dielectric media.
Inputs
Select unit scaling: 1 µC = 10⁻⁶ C, 1 nC = 10⁻⁹ C, 1 e = +1.602×10⁻¹⁹ C.
Used to derive force F = q·E and potential energy U = q·V.
Preset Scenarios
Electric field & potential
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Enter a charge and distance to compute the field strength and potential.
Field Strength (E)—
Field Strength (V/m)—
Electric Potential (V)—
Force on Test Charge (F)—
Potential Energy (U)—
Dielectric Medium (εᵣ)—
Force on a charge in a field
Note: 1 N/C is equivalent to 1 V/m.
Force on the charge
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Enter a field strength and charge to compute the electrostatic force.
Solve for distance
Solves E = k·q / (εᵣ·r²) for distance: r = √(k·|q| / (εᵣ·E)).
Distance from charge
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Enter a charge and a target field strength to solve for the distance.
Particle Dynamics in Field
C
kg
Calculates electrostatic force F = q·E and acceleration a = F / m in a uniform field.
Particle Acceleration
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Enter electric field strength to calculate particle acceleration.
Acceleration (a)—
g-Force Equivalent—
Electrostatic Force (F)—
Particle Charge (q)—
Particle Mass (m)—
✓ Scientifically Verified
Last Verified: July 2026•Next Review: July 2027
Physical Standards & Academic References
This calculator uses internationally recommended CODATA 2022 / NIST physical constants for precision calculations in physics and electrical engineering.
Elementary Charge (e)1.602 176 634 × 10⁻¹⁹ C (2019 SI Base Unit Definition)
Academic Reference TextbooksHalliday, Resnick & Walker, Fundamentals of Physics (12th Ed., Ch. 22); Serway & Jewett, Physics for Scientists and Engineers.
Educational & Laboratory Disclaimer: Intended for academic physics education, laboratory work, and engineering coursework. For industrial high-voltage breakdown design, dielectric insulation testing, or transmission line safety compliance, refer to official IEEE / IEC engineering standards.
An electric field is a fundamental force field surrounding every electric charge.
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Walk-through
How to Use This Calculator
3 steps▸
1
Select Calculation Mode & Medium
Choose whether to calculate the electric field strength E from a point charge and distance (E = k·q / r²), from measured electrostatic force per charge (E = F / q), or solve backward for distance (r = √(k·|q| / E)). You can also select the surrounding medium (vacuum, air, water, glass, or silicon).
2
Enter Values & Unit Scale
Enter the source charge (in C, µC, nC, pC, or e) and distance (in m, cm, mm, µm, nm, or Å). You can also provide a test charge to view the electrostatic force F = q·E exerted on it.
3
Review Field Strength & Kinematics
The calculator displays electric field strength in N/C and V/m, electric potential V in Volts, electrostatic energy U, field vector direction, and particle acceleration (a = qE/m) for electrons or protons.
Coulomb's Law formulation for the electric field produced by a point charge q at a radial distance r in a dielectric medium of relative permittivity εr. Coulomb's constant k ≈ 8.9875517923 × 10⁹ N·m²/C².
Field Strength from Force per Unit Charge
E = \frac{F}{q_{\text{test}}}
The fundamental field definition: electric field vector E is the electrostatic force F experienced per unit positive test charge placed at that location.
Force on a Charge in a Field
F = q \cdot E
The force exerted by an electric field E on any charge q. Positive charges experience force in the field direction; negative charges experience force opposite to the field direction.
Electric Potential & Potential Energy
V = \frac{k \cdot q}{\varepsilon_r \cdot r}, \quad U = q_{\text{test}} \cdot V = \frac{k \cdot q \cdot q_{\text{test}}}{\varepsilon_r \cdot r}
Electric potential V (in Volts) produced by a point charge, and the electrostatic potential energy U (in Joules or eV) stored in the two-charge system.
Charged Particle Kinematics
a = \frac{q \cdot E}{m}, \quad K = q \cdot \Delta V = \frac{1}{2} m v^2
Newton's second law applied to a charged particle of mass m and charge q in a uniform electric field E, calculating acceleration and kinetic energy gain.
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Glossary
Key Terms Explained
6 terms▸
Electric Field Strength (E)A vector field representing the electric force per unit charge exerted on a positive test charge at a point in space, measured in Newtons per Coulomb (N/C) or Volts per metre (V/m).
Coulomb's Constant (k)The proportionality constant in electrostatic equations, k = 1/(4πε₀) ≈ 8.9875517923 × 10⁹ N·m²/C², derived from the speed of light and vacuum permeability.
Permittivity of Free Space (ε₀)The physical constant representing the capability of classical vacuum to permit electric field lines, ε₀ ≈ 8.8541878128 × 10⁻¹² F/m (or C²/(N·m²)).
Relative Permittivity / Dielectric Constant (εᵣ)A dimensionless ratio indicating how much a medium reduces the net electric field compared to vacuum (εᵣ = 1 for vacuum, ~1.00059 for air, 80 for water, 3.9 for silica glass).
Electric Potential (V)The electrostatic potential energy per unit charge at a point in space, measured in Volts (1 V = 1 J/C = 1 N·m/C).
Test Charge (q)An idealized, infinitesimally small charge used to probe the magnitude and direction of an electric field without altering the source charge distribution.
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Scenarios
Real-World Examples
3 worked examples▸
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Physics Student calculating field strength around a microcoulomb charge
1 µC charge at 10 cm in air
Point Charge (q) 1 µCDistance (r) 10 cmMedium Air (εᵣ = 1.0006)
E = (8.98755 × 10⁹ × 10⁻⁶) / (1.0006 × 0.1²) ≈ 898,225 N/C (or V/m). The field points radially outward from the positive charge.
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Atomic Physicist measuring atomic electric field at Bohr radius
Proton (+e) at 0.0529 nm (Bohr radius)
Charge (q) +e (1.602 × 10⁻¹⁹ C)Distance (r) 0.529 Å (5.2918 × 10⁻¹¹ m)
E ≈ 5.14 × 10¹¹ N/C. The immense electric field at atomic scale holds the electron bound to the nucleus with an electric potential V ≈ 27.2 V.
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Electrical Engineer checking electron acceleration in CRT or ion thruster
Electron in a 1,000 N/C uniform field
Field Strength (E) 1,000 N/CParticle Electron (q = -e, m = 9.109 × 10⁻³¹ kg)
Force F = 1.602 × 10⁻¹⁶ N. Acceleration a = F / m ≈ 1.759 × 10¹⁴ m/s², directed opposite to the electric field lines.
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Deep Dive
Understanding Electric Fields, Coulomb's Law, and Electrostatic Forces
3 chapters · 2 min read▸
An electric field is a fundamental force field surrounding every electric charge. It dictates the force that other charges experience when placed within its influence. From atomic bonding in chemistry to semiconductor transistors, CRT tubes, and high-voltage transmission lines, calculating electric field strength is essential in physics and electrical engineering.
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Questions
Frequently Asked Questions
4 questions▸
What is the difference between N/C and V/m?+
There is no physical or mathematical difference! 1 Newton per Coulomb (N/C) is identically equal to 1 Volt per metre (V/m). N/C emphasizes force per charge, while V/m emphasizes spatial rate of voltage change.
Why does distance cannot be zero in the point charge formula?+
The point charge equation E = k·q/r² assumes an ideal point with zero volume. As r approaches 0, E approaches infinity. Real physical charges (like electrons or atomic nuclei) are governed by quantum mechanics or finite charge distributions at subatomic scales.
How does a dielectric medium affect electric field strength?+
In a dielectric medium (such as water, glass, or plastic), electric dipoles align against the external field. This polarization creates an internal counter-field, weakening the net field by a factor of the material's relative permittivity (εᵣ). For instance, in water (εᵣ = 80), the electric field strength is reduced by 98.75% compared to vacuum.
What direction does the electric field point?+
By convention, electric field vectors point radially OUTWARD from positive charges and radially INWARD toward negative charges. A positive test charge will accelerate along the field lines, whereas a negative charge will accelerate opposite to field lines.
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