The electric field produced by a single point charge is one of the most fundamental results in classical electromagnetism. Using Coulomb's constant , the magnitude of the electric field at a distance from a charge is given by . If any two of these variables are known, the third can be isolated algebraically and calculated instantly. Our calculator implements these relations directly in your browser with no network connection, ensuring privacy and speed.
Electric fields describe how a charge influences the surrounding space. Another charge placed in this field feels a force , pointing radially outward for a positive source charge and inward for a negative one. Historically, Michael Faraday visualized electric fields as lines emanating from charges. James Clerk Maxwell later unified the concepts of electricity and magnetism, expressing electric fields in a set of differential equations still used today. The simplicity of the point charge solution makes it ideal for textbook examples and real-world approximations when charges are small compared with the distances involved. Because Coulomb's law obeys an inverse-square form, the field diminishes quickly; doubling the distance reduces the field strength by a factor of four.
While the calculation is straightforward, the underlying physics invites deeper exploration. Electric fields are vector quantities, meaning they possess both magnitude and direction. The direction is radial, so in three-dimensional space the field at any point is oriented along the line connecting that point to the source charge. In practical applications, we often superimpose contributions from multiple point charges using vector addition. Although our calculator focuses on a single charge, the concept scales linearly because Coulomb's law is additive: the field from many charges is the vector sum of the fields from each charge individually. This principle forms the basis for analyzing charge distributions such as dipoles, lines, and sheets, which are tackled in more advanced calculators within this collection.
The units deserve special attention. Charge is measured in coulombs (C), a surprisingly large quantity compared with everyday static charges, which are typically microcoulombs or nanocoulombs. Distance is in meters, and the resulting field strength is newtons per coulomb, the force on a 1-C test charge. Because charges of that magnitude are unrealistic, scientists often think in terms of the force on a single elementary charge: dividing by the elementary charge converts to electronvolts per meter, a more intuitive scale in atomic physics. When performing calculations in our form, enter numerical values using scientific notation if needed (for example, 1e-6 for one microcoulomb) to maintain accuracy over wide ranges.
To operate the calculator, supply any two quantities and leave the third field empty. If you know the charge and distance, the script computes the electric field. If you know the field and distance, it determines the charge responsible. If you know the charge and field, it solves for the radius at which that field is observed. The algorithm checks inputs, ensures exactly one field is blank, and displays the result with proper units. All math occurs locally in JavaScript. This self-contained approach prevents data transmission and enables use even when offline.
Why study electric fields of point charges? Many high school and undergraduate problems involve analyzing the forces between two charges or evaluating the field at a point in space. Understanding how fields scale with distance provides intuition for shielding, capacitance, and atomic structure. For instance, the strong field near an atomic nucleus influences electron energy levels. In particle accelerators, precise control of electric fields guides beams of charged particles. Even everyday phenomena such as static cling and lightning strikes rely on the same mathematical foundation that governs our simple equation.
Consider an example: suppose you want to find the field 5 cm away from a 2 μC charge. Plugging into the formula yields , approximately 7.2×106 N/C. This value indicates a very strong field close to the charge. If instead you observe an electric field of 1,000 N/C at a distance of 1 m and wish to determine the source charge, rearranging gives , resulting in roughly 1.11×10-8 C, or 11 nC. Solving such problems repeatedly builds familiarity with orders of magnitude and typical scales encountered in electrostatic setups.
The table below lists sample values to further illustrate how electric field strength diminishes with distance for a fixed 1 μC charge. Notice the inverse-square trend: halving the distance multiplies the field by four. Values are rounded for clarity.
| Distance (m) | Field (N/C) |
|---|---|
| 0.10 | 8.99 × 104 |
| 0.20 | 2.25 × 104 |
| 0.40 | 5.62 × 103 |
| 0.80 | 1.40 × 103 |
In advanced courses, point charge fields serve as building blocks for solving Maxwell's equations via Green's functions and multipole expansions. While such topics extend beyond the scope of this introductory calculator, they highlight the versatility of Coulomb's law. By mastering the simple expression here, students lay the groundwork for tackling complex electrostatic configurations, understanding dielectric effects, and analyzing potential energy landscapes in both classical and quantum contexts.
Whether you're verifying homework, designing an experiment, or satisfying curiosity about the invisible forces around charged objects, this calculator provides a convenient tool. Because it runs entirely on client-side code, you can bookmark the page, share it with classmates, or adapt it for teaching demonstrations without worrying about external dependencies. The combination of numerical computation and extensive explanatory text makes it not just a calculator but also a mini-tutorial on the physics of point charges. Experiment with different values to see how changing charge or distance affects the field, and let these insights guide deeper explorations into electromagnetism.