Understanding electric charge is foundational to both everyday life and advanced engineering. From the static spark that lights your hair to the currents that power smartphones, mastering how to compute charge equips you with the tools to analyze, design, and troubleshoot electrical systems with confidence.
While several equations can be used in different contexts, the most ubiquitous formula is Coulomb’s Law. It relates the force between two point charges to the magnitude of each charge and their separation.
FE = k q1 q2 / r²
where k = 8.987 × 10⁹ N·m²/C² (often rounded to 9.0 × 10⁹) is Coulomb’s constant, q1 and q2 are the charges in coulombs, and r is the distance between them in meters. Electrons carry a charge of –1.602 × 10⁻¹⁹ C, while protons carry +1.602 × 10⁻¹⁹ C.
For like charges (both positive or both negative) the force is repulsive; for opposite charges it is attractive. The magnitude of the force scales linearly with the product of the charges.
Coulomb’s Law mirrors Newton’s Law of Universal Gravitation:
FG = G m1 m2 / r²
Both equations feature an inverse-square dependence on distance, yet gravity is always attractive while electrostatic forces can be attractive or repulsive. The relative strengths differ by many orders of magnitude: the electromagnetic force is roughly 10²⁰ times stronger than gravity, underscoring why local electric effects dominate over gravitational ones in most engineering applications.
In an isolated system, the total charge remains constant. This principle enables engineers to predict charge distribution and to design shielding such as Faraday cages, which redirect external electric fields around a protected volume. Faraday cages are essential in MRI machines and in protective gear for high‑voltage workers.
Because an electron’s charge is –1.602 × 10⁻¹⁹ C, a charge of –8 × 10⁻¹⁸ C corresponds to:
n = |Q| / |e| = 8 × 10⁻¹⁸ C / 1.602 × 10⁻¹⁹ C ≈ 50 electrons
The total charge that flows through a circuit is the product of current and time:
Q = I t
where I is current in amperes and t is time in seconds. Current itself can be found from Ohm’s Law, V = I R.
Example: A 3 V source across a 5 Ω resistor applied for 10 s yields
– I = V/R = 3 V / 5 Ω = 0.6 A
– Q = I t = 0.6 A × 10 s = 6 C
Alternatively, if voltage and work (energy) are known, charge can be computed as Q = W / V.
The electric field is defined as force per unit charge:
E = FE / q
This quantity governs how charges move and how forces are distributed in space. Even a neutrally charged object can sustain internal charge distributions, leading to polarization and bound charges.
Observations of cosmological phenomena indicate the universe is electrically neutral to a high degree. If a net charge existed, the resulting large‑scale electric fields would produce measurable effects on cosmic microwave background anisotropies and the trajectories of charged particles across interstellar distances. The lack of such signatures supports the prevailing view that the universe’s total charge sums to zero.
Electric flux through a surface is the integral of the field over that area. For a planar surface, the flux simplifies to:
Φ = E A cos θ
where A is the area, and θ is the angle between the field and the surface normal. Gauss’s Law states that the flux through any closed surface equals the enclosed charge divided by ε₀, linking geometry to charge content.
Static electricity arises when objects acquire an excess of electrons or protons, often through friction (e.g., rubbing a balloon on hair). The resulting non‑equilibrium charges can cause sparks, levitating objects, or damage to sensitive electronics. Neutralization—through grounding or conductive surfaces—restores equilibrium.
Conductors (e.g., copper, aluminum) allow electrons to move freely, so any internal electric field is immediately cancelled by charge redistribution. This yields zero field inside and a uniform surface charge distribution on symmetric shapes. Insulators (e.g., wood, glass) impede charge flow, maintaining static charges until they dissipate. Semiconductors sit between conductors and insulators, with charge transport controlled by doping and temperature.
Gauss’s Law is particularly powerful for systems with high symmetry. For a long, uniformly charged cylinder, the electric field outside is perpendicular to the surface and given by E = σ / ε₀, where σ is surface charge density. Inside a perfect conductor, E = 0, ensuring no net charge resides within.
