Point Charge Electric Field

Electric field: E = k·Q/r²

The electric field tells you the force per unit charge at a point in space: E = F/q = k·Q/r² (magnitude), with k = 8.99·10⁹ N·m²/C². It's a vector, pointing radially outward from a positive source charge and inward toward a negative one (roughly, "from + to −"). The units are N/C, or equivalently V/m. Field lines never cross, and inside a conductor in electrostatic equilibrium E = 0, because the free charges rearrange to cancel the internal field. Got more than one charge? Apply the superposition principle and add the individual contributions as vectors. In a parallel-plate capacitor the field comes out uniform: E = V/d or E = σ/ε₀, where σ is the surface charge density. Example: Q = 1 nC at r = 1 m gives E = (8.99·10⁹)(10⁻⁹)/1² = 8.99 V/m. Push the field hard enough and air breaks down, turning into a conductor and giving you lightning or sparks, at roughly 3 MV/m, the limiting dielectric strength.

Applications

Lasers and cathode ray tubes (old TVs and oscilloscopes, where electrons get steered by E fields), particle accelerators like the LHC, electrostatic powder coating of paint, copiers and laser printers (charged toner pulled toward a charged drum), capacitor design, haptic feedback in touchscreens, electric dust filters in industrial chimneys, and modeling lightning discharges, where the cloud-to-ground potential difference reaches around 10⁹ V.

FAQ

What's the difference between E and V? V (volts) is the electric potential, the energy per unit charge. E (V/m) is the field itself, which equals the negative gradient of V. A potential difference drives a force on charges, but a charge only feels a push where E is nonzero.

Why is E = 0 inside a conductor? At equilibrium, the conductor's free electrons shift around on the surface until the internal field cancels out completely. That same effect is what lets a Faraday cage shield its interior from outside fields, which is why you find them in MRI rooms, the walls of a microwave oven, and shielded cables.

Can the field be infinite? On paper, E → ∞ as r → 0 for a point charge. In reality, charges have a finite size (the electron radius), and once fields climb high enough air ionizes (above 3 MV/m) and the model stops working. The strong-field regime is the domain of quantum electrodynamics.