Dipole Field Simulator
Explore electric dipole field lines, compute dipole moments (p = q·d), and animate rotational torque (τ = p × E) in an external electrostatic field.
What is an Electric Dipole?
An electric dipole consists of a pair of equal in magnitude but opposite in sign point electrical charges (+q and -q) separated by a finite distance d. The characteristic quantity of this system is the electric dipole moment vector p, directed from the negative pole to the positive pole:
Dipoles are ubiquitous across chemistry and electrodynamics. Molecular water (H₂O) has a permanent electric dipole moment of 1.85 Debye due to the electronegativity difference between oxygen and hydrogen, making it the primary mechanism for microwave heating and solvent solvation.
How to Use the Dipole Field Simulator
Model dipole configurations and observe rotational torque mechanics in four easy steps.
Set Charge Magnitude
Adjust the charge slider (q) to scale the strength of the dipole electric field.
Adjust Separation
Vary distance (d) to explore short-range near fields versus long-range 1/r³ far-field decay.
Apply External Field
Introduce an external uniform electric field to induce restoring torque (τ = p × E).
Simulate Oscillation
Click 'Simulate Torsional Oscillation' to watch the dipole swing like a torsional pendulum seeking equilibrium.
Key Interactive Features
Engineered for electromagnetic physics instruction and engineering research.
Torque & Energy Metrics
Calculates instantaneous restoring torque in N·m and electrostatic potential energy in Joules.
Continuous Loop Tracing
Dynamically traces closed-loop field lines radiating from the positive charge and terminating on the negative charge.
Torsional Dynamics
Includes physical moment of inertia and angular damping to simulate realistic harmonic alignment.
Dipole Field & Torque Equations
Along the axial line of a dipole at distance r >> d, the electric field is directed parallel to p:
Along the equatorial perpendicular bisector at distance r >> d, the field is antiparallel to p and exactly half as strong:
When placed in a uniform external field E, the net force is zero (F_net = 0), but the net torque and potential energy are:
Scientific & Industrial Applications
Microwave Ovens & Dielectric Heating
Microwave ovens generate a rapidly alternating electric field oscillating at 2.45 GHz. Water molecules in food continually rotate to align their dipole moments with the shifting field, dissipating rotational energy as thermal heat that cooks food rapidly from the inside out.
Cardiac Vectorcardiography (ECG)
As cardiac muscle tissue depolarizes and repolarizes during every heartbeat, the wave of electrical excitation behaves as a rotating heart dipole vector. Electrodes attached to a patient's chest measure the projected electric potential differences, forming the electrocardiogram (ECG/EKG) trace.
Frequently Asked Questions
An electric dipole moment is a vector quantity (p = q * d) representing a pair of equal and opposite charges (+q and -q) separated by a distance d. By physics convention, the dipole vector points from the negative charge to the positive charge.
In a uniform electric field, the positive charge experiences a force F+ = qE in the field direction, while the negative charge experiences an equal and opposite force F- = -qE. Because these forces act along different lines of action separated by distance d, they produce a net torque τ = p × E that attempts to align the dipole with the field.
Unlike a single point charge whose field decays as 1/r², a dipole's electric field drops off much more rapidly as 1/r³ at distances large compared to the charge separation. This is because the fields from the opposing positive and negative charges largely cancel each other out from afar.
The potential energy of a dipole in an external field is U = -p · E = -pE cos(θ). It reaches a minimum of -pE at θ = 0° (stable equilibrium, parallel to the field) and a maximum of +pE at θ = 180° (unstable equilibrium, antiparallel to the field).