# Electric Field of a Point Charge

E = k·|Q|/r² in N/C with charge and distance unit selectors, the radial direction from the sign of Q, and the force an electron would feel at that point.

> Canonical page: https://elysiatools.com/en/tools/electric-field-point-charge

- **Category:** Science & Education

- **Keywords:** electric field, point charge, field strength, coulombs law, newtons per coulomb, electromagnetism

## Overview

The Electric Field of a Point Charge calculator computes electric field magnitude and radial direction using Coulomb's constant via E = k·|Q|/r². It supports multiple charge and distance units while calculating the electrostatic force experienced by a test electron at that position.

## Inputs

- **Charge Q** (number): e.g. 1
- **Charge unit** (select)
- **Distance r** (number): e.g. 1
- **Distance unit** (select)

## When to use

- When solving introductory electromagnetism and physics problem sets involving point source charges.
- When determining the radial field strength and direction produced by static charges across various metric distance scales.
- When calculating the exact electrostatic force exerted on an electron placed at a specified radius from a source charge.

## How it works

- Enter the source charge value Q and select the appropriate metric charge unit from Coulombs down to picocoulombs.
- Input the radial distance r and choose the distance unit ranging from meters to nanometers.
- The tool applies Coulomb's constant to evaluate E = k·|Q|/r², determines field vector orientation based on the charge sign, and computes the test electron force F = e·E.

## Use cases

- Physics education: Calculating electric field vectors and electrostatic attraction or repulsion forces for homework problems.
- Atomic physics demonstrations: Evaluating microscopic electric fields near fundamental charges at sub-nanometer distances.
- Electrostatic lab modeling: Estimating static charge field gradients and sensor response thresholds during laboratory setups.

## Frequently asked questions

### What equation is used to calculate the electric field?

It uses Coulomb's law for electric fields, E = k·|Q|/r², where k is Coulomb's constant (approximately 8.98755×10⁹ N·m²/C²).

### How does the sign of the charge affect the result?

The sign of Q determines the field direction: positive charges produce fields pointing radially outward, while negative charges point radially inward.

### Are the units N/C and V/m equivalent?

Yes, Newtons per Coulomb (N/C) and Volts per meter (V/m) are dimensionally identical measures of electric field strength.

### How is the force on an electron calculated?

The force is determined by multiplying the elementary charge e (1.602176634×10⁻¹⁹ C) by the field magnitude E (F = e·E).

### Which units of distance and charge are supported?

Charge supports C, mC, µC, nC, and pC. Distance supports m, cm, mm, µm, and nm.

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