Interactive 3D Visualization of Magnetic Field Intensity & Lorentz Force Direction
Ampere's Circuital Law
∮ H · dl = Ienc
The circulation of magnetic field intensity around
a closed path is equal to the current enclosed by
that path.
⚡ Applied Force & Current Calculator
Enter your own values. The program calculates the
current required to produce the applied force and
visualizes the exact magnetic force direction vector in 3D.
Select Applied Force Direction (F = I L × B):
Calculated Result & Vector Direction Analysis
Applied Force Magnitude |F|:
10 N
Magnetic Flux Density B:
0.000126 T
Calculated Current I:
79577.47 A
Angle θ (I, B):
90°
Selected Force Vector F:
+X Vector (→)
Right-Hand Rule Relation:
F = I L × B
System Movement Direction:
+X direction →
Enter your values and click
CALCULATE & APPLY FORCE.
🖱 Drag to rotate • Scroll to zoom • Orange arrow = Force F • Yellow = Current I • Blue = Field B
Infinite Line Current
A long straight conductor carrying current I
produces circular magnetic field intensity
around the conductor.
Hφ =
I / (2πρ)
Use the right-hand thumb rule to determine
the direction of H.
Infinitely Long Coaxial Transmission Line
Consider an infinitely long coaxial transmission
line consisting of two concentric cylindrical
conductors having their axes along the z-axis.
The inner conductor has radius a and carries
current +I. The outer conductor has inner
radius b, thickness t, and carries
return current −I.
Region 1 — Ampere Path L1
0 ≤ ρ ≤ a
Hφ =
Iρ / (2πa²)
Region 2 — Ampere Path L2
a ≤ ρ ≤ b
Hφ =
I / (2πρ)
Region 3 — Ampere Path L3
b ≤ ρ ≤ b + t
Hφ =
I / (2πρ)
[1 − (ρ² − b²)/(t² + 2bt)]
Region 4 — Ampere Path L4
ρ ≥ b + t
Hφ = 0
Final Result
H =
Iρ/(2πa²) ,
0 ≤ ρ ≤ a
I/(2πρ) ,
a ≤ ρ ≤ b
I/(2πρ)
[1 − (ρ² − b²)/(t² + 2bt)]
,
b ≤ ρ ≤ b+t
0 ,
ρ ≥ b+t
Force Vector & Right-Hand Rule Visualization
When a current-carrying conductor is placed in a
magnetic field, the magnetic force direction is given by the cross product:
F = I L × B
|F| = B I L sinθ
B = μ0H
I = |F| / (μ0 H L sinθ)
• Yellow Arrow / Particles: Direction of Current Flow ($I$)
• Cyan / Blue Arrows: Direction of Magnetic Field Intensity ($H, B$)
• Orange Arrow: Direction of Resultant Force Vector ($F$)
• Movement Trail: Real-time displacement along the force vector axis.
Practical Applications
⚙ Electric Motors
Magnetic fields produced by current-carrying
conductors help produce rotational force.
🔌 Transformers
Magnetic fields produced by coils are used
to transfer electrical energy.
📡 Coaxial Cables
Ampere's law is used to determine magnetic
field intensity in coaxial transmission lines.
🌀 Solenoids
Ampere's law helps determine the magnetic
field inside long current-carrying coils.
🧲 Electromagnets
Current through coils produces magnetic
fields used in many electrical devices.
📶 Communication Systems
Coaxial transmission lines are used to
carry electrical and high-frequency signals.