⚡ Magnetic Field Analyzer

📘 About This Simulation

This tool visualizes the magnetic field generated by three-phase AC conductors in real-time. It calculates and displays the time-varying electromagnetic field using Ampère's law, showing how the field rotates and changes magnitude as the currents oscillate through their AC cycles.

🎮 How to Use

Interact with Conductors:

• Click and drag any conductor (A, B, or C) to reposition it
• Dragging automatically pauses the animation
• Release to recalculate and resume animation
• Adjust "Triangle Spacing" slider to set the size of the equilateral triangle
• Use "Center Equilateral Triangle" to arrange conductors symmetrically at the chosen spacing

Navigate the View:

• Click and drag the background to pan the view
• Scroll to zoom in/out
• Use the Zoom slider for precise control

Observe Field Cancellation:

• The yellow center marker shows the geometric center of the three conductors
• The "Center Point Field" panel displays the magnetic field strength at this center
• For a balanced three-phase system in equilateral arrangement, the center field should be near zero!
• Adjust the "Triangle Spacing" slider to change conductor separation (0.1 to 2.0 meters)
• Try the "Center Equilateral Triangle" button to see perfect field cancellation at any spacing
• Note: Smaller spacing increases mutual coupling and changes the GMD calculations

Explore Field at Any Point:

• Move your cursor over the canvas to see real-time field measurements at that location
• The "Cursor Position Field" panel shows field magnitude, components (Bx, By), and direction
• Watch how the field changes as you move around the conductors

Adjust Parameters:

• Change frequency (50-400 Hz) to see different AC rates
• Modify phase angles to create unbalanced systems
• Adjust currents to see field strength changes
• Change conductor radii to affect inductance

🔢 Calculations Explained

Magnetic Field (Ampère's Law):

B = (μ₀ × I) / (2π × r)

The magnetic flux density at distance r from a conductor carrying current I, where μ₀ = 4π×10⁻⁷ H/m is the permeability of free space.

Instantaneous Current:

i(t) = I × sin(2πft + φ)

Where I is the RMS current magnitude, f is frequency (Hz), t is time (s), and φ is the phase angle (radians).

Geometric Mean Distance (GMD):

GMD = ∛(D_AB × D_BC × D_CA)

The cubic root of the product of all conductor spacing distances. Used to calculate mutual inductance between phases.

Geometric Mean Radius (GMR):

GMR = 0.7788 × r

For a solid cylindrical conductor of radius r. GMR accounts for internal flux linkage and is used in self-inductance calculations.

Self Inductance per meter:

L_self = (μ₀/2π) × ln(1/GMR)

The inductance of a single conductor due to its own current, per unit length.

Mutual Inductance per meter:

L_mutual = (μ₀/2π) × ln(1/D)

The inductance between two conductors separated by distance D, per unit length.

Inductive Reactance:

X = 2πfL

The opposition to current flow due to inductance L at frequency f. Measured in ohms per meter (Ω/m).

Positive Sequence Reactance:

X₁ = X_self - X_mutual_avg

Reactance experienced by balanced three-phase currents. Used in normal operating conditions.

Zero Sequence Reactance:

X₀ = X_self + 2×X_mutual_avg

Reactance when all phases carry equal in-phase currents (ground faults). Always higher than X₁ due to additive mutual coupling.

Coupling Factor:

The simulation indicates coupling strength based on GMD:

• Very High (GMD < 0.3m): Strong magnetic interaction
• High (0.3-0.6m): Significant coupling
• Medium (0.6-1.0m): Moderate coupling
• Low (GMD > 1.0m): Weak coupling

🎨 Visualization Elements

• Field Lines: Follow the direction of magnetic flux
• Intensity Contours: Show equal-strength field boundaries
• Field Vectors: Display field direction and magnitude
• Heat Map: Color intensity indicates field strength
• Phasor Diagram: Shows rotating current vectors with brightness proportional to instantaneous current
• Geometric Center (Yellow): Marks the center point of the three conductors where field cancellation occurs in balanced systems

Color Scale: Yellow/green = strong field, blue/purple = weak field. The scale adapts to show detail across the entire range.