Electric Field Simulator
Visualize Coulomb's law electric field lines, vector grids, and test charge kinematics. Drag source charges, watch particles accelerate, and probe field strength dynamically.
What is an Electric Field?
An electric field is an invisible physical vector field surrounding electrically charged particles. It exerts an electrostatic force on any other charge brought into its vicinity, described mathematically by Coulomb's Law. Electric field lines radiate outward from positive charges and converge inward onto negative charges.
Unlike scalar quantities like electric potential, the electric field has both magnitude and spatial direction at every coordinate. In this simulator, field lines are calculated through continuous numerical integration, showing how positive test particles accelerate along field lines and experience curved trajectory deflection.
How to Use the Electric Field Simulator
Explore electromagnetic vector mechanics in four straightforward steps.
Add or Move Charges
Drop +6 nC or -6 nC charges onto the canvas or drag existing ones to observe field line restructuring.
Adjust Line Density
Scale the ray count slider to inspect high-resolution field mapping and convergence near poles.
Observe Particle Motion
Watch the yellow test charge follow Newton's second law F = qE = ma with realistic kinematic damping.
Sample Field Vectors
Click anywhere on the grid to instantly measure local electric field intensity in V/m and angle in degrees.
Key Interactive Features
High-performance vector simulation designed for physics education and conceptual mastery.
Coulomb Vector Superposition
Calculates cumulative vector field Ex and Ey from every active source charge in real time.
Dynamic Particle Kinematics
Animates a charged test particle subjected to real electrostatic acceleration with velocity path history.
Field Probe Sensor
Instant telemetry calculates magnitude in V/m and vector angle θ relative to the horizontal axis.
Coulomb's Law & Vector Field Mathematics
The electric field E produced by a point charge q at a distance r is given by Coulomb's Law:
Where 1/(4πε₀) ≈ 8.9875 × 10⁹ N·m²/C² is Coulomb's constant. For N point charges, the total electric field at coordinate (x, y) is the vector sum:
When a particle with mass m and charge q_0 enters this field, the electrostatic force F = q_0 · E dictates its instantaneous acceleration a = F / m.
Engineering & Industrial Applications
Industrial Electrostatic Precipitators
Smokestacks use intense electric field gradients to ionize airborne smoke particles and fly ash, attracting them to grounded collection plates to eliminate over 99% of particulate emissions before reaching the atmosphere.
Continuous Inkjet (CIJ) Printing
Industrial high-speed inkjet printers shoot microscopic ink droplets through an electrostatic charging electrode. Variable deflection plates create a dynamic electric field that steers individual droplets onto packages at thousands of drops per second.
Frequently Asked Questions
Electric field lines are imaginary curves whose tangent at any point indicates the direction of the electric field vector E at that location. The spatial density (closeness) of the lines is proportional to the magnitude (strength) of the electric field.
At any specific point in space, the net electric field has one unique direction determined by the vector sum of all contributing charges. If two field lines crossed, it would imply two different directions of electric force at a single point, which is physically impossible.
A positive test charge experiences a force parallel to the electric field (F = qE), while a negative charge experiences a force antiparallel to the field. According to Newton's second law (F = ma), this force causes the particle to accelerate along its curved trajectory.
The simulator computes the superposition of electric fields from all source charges using Coulomb's law E = (1 / 4πε₀) * (q / r²). For each field line, numerical integration (Euler or Runge-Kutta stepping) traces the trajectory tangent to the resultant field vector.