Quadratic Equation Solver (ax² + bx + c = 0)
About Electric Field Calculator
The Electric Field Intensity ($\vec{E} = \frac{\vec{F}}{q} = k_e \frac{Q}{r^2}$) Calculator computes vector electric field strength around point charges, uniform electric fields between parallel plates ($E = V/d$), line charges (Gauss's Law $E = \frac{\lambda}{2\pi\varepsilon_0 r}$), and electric dipole fields.
How to Use Electric Field Calculator
Step 1
Select Field Source (Point Charge, Parallel Plates, or Dipole).
Step 2
Enter charge/voltage and distance parameters.
Step 3
Review computed field intensity, electron acceleration, and dielectric safety.
Step 4
Click "Copy Electric Field".
Practical Use Cases for Electric Field Calculator
Capacitor Dielectric Breakdown & High-Voltage Spark Gap Sizing
Calculate electric field stress ($V/m$) across capacitor insulator layers to verify dielectrics stay below breakdown voltage limits ($3\text{ MV/m}$ in air).
Cathode Ray Tube (CRT) & Mass Spectrometer Ion Deflection
Compute electric acceleration on charged electrons and protons traveling between charged deflection plates ($a = qE/m$).
Input & Output Examples
Calculating Field Between Parallel Plates (500V across 2mm gap)
Voltage ($V$): `500.0 V`, Plate Gap ($d$): `2.0 mm (0.002 m)`
Electric Field ($E$): `250,000 V/m (250 kV/m)` | Acceleration on Electron: `4.39 × 10¹⁶ m/s²` | Air Breakdown Safety: `Safe (< 3 MV/m)`
Key Features & Performance
- ✓Modes: Point Charge ($k Q / r^2$), Parallel Plate Uniform Field ($V/d$), Infinite Line Charge (Gauss), Electric Dipole Moment.
- ✓Charged Particle Kinematics: computes electrostatic force ($F=qE$) and acceleration ($a=F/m$) for electrons, protons, and alpha particles.
- ✓Unit conversions: Volts per meter (V/m), Newtons per Coulomb (N/C), Kilovolts per millimeter (kV/mm).
- ✓100% Client-Side electromagnetism engine.
- ✓1-Click Copy electric field specs.
Key Terminology & Definitions
Electric Field ($\vec{E}$)
A vector field surrounding an electric charge that exerts a force on other charged objects, measured in Volts per meter (V/m) or Newtons per Coulomb (N/C).
Dielectric Breakdown
The electrical failure of an insulating material when the electric field strength exceeds the material's dielectric limit, causing ionization and sparking.