Calculator Input Panel
The page uses a single stacked layout, while the calculator fields expand to three columns on large screens, two on smaller screens, and one on mobile.
Example Data Table
These sample cases show how the different methods produce magnetic induction values under common engineering and physics-style inputs.
| Method | Example Inputs | Formula | Computed Output |
|---|---|---|---|
| Straight wire | I = 10 A, r = 0.05 m, μr = 1 | B = μI / (2πr) | 4.000000e-5 T (0.04 mT) |
| Solenoid | N = 800, I = 1.5 A, L = 0.4 m, μr = 1 | B = μNI / L | 0.00377 T (3.769911 mT) |
| Circular loop | N = 20, I = 3 A, R = 0.08 m, μr = 1 | B = μNI / (2R) | 0.000471 T (0.471239 mT) |
| Toroid | N = 300, I = 2 A, r = 0.12 m, μr = 1 | B = μNI / (2πr) | 0.001 T (1 mT) |
| Force on conductor | F = 0.6 N, I = 5 A, L = 0.3 m, θ = 90° | B = F / (ILsinθ) | 0.4 T (400 mT) |
| Flux density | Φ = 0.002 Wb, A = 0.01 m², θ = 0° | B = Φ / (Acosθ) | 0.2 T (200 mT) |
Formula Used
Straight wire
B = μI / (2πr)
Use this for a long straight conductor. The field drops as distance from the wire increases.
Long solenoid
B = μNI / L
This estimates the nearly uniform internal field of a long solenoid with many turns.
Circular loop center
B = μNI / (2R)
Use this for the magnetic induction at the geometric center of a circular loop.
Toroid
B = μNI / (2πr)
This uses the mean magnetic path radius to estimate the internal toroidal field.
Moving charge force
B = F / (|q|v sinθ)
Rearranges the magnetic force equation to determine the field from measured force data.
Current-carrying conductor force
B = F / (IL sinθ)
Useful when the magnetic force on a conductor segment is measured experimentally.
Magnetic flux relation
B = Φ / (A cosθ)
Use this when magnetic flux, area, and orientation angle are known.
Energy density relation
u = B² / (2μ) → B = √(2μu)
This derives induction from magnetic energy stored per unit volume in a medium.
Symbols
B = magnetic induction or magnetic flux density
μ = magnetic permeability = μ₀μr
μ₀ = permeability of free space = 4π × 10-7 H/m
μr = relative permeability of the material
I = current, N = number of turns, L = length
r or R = radius, F = force, q = charge
Φ = magnetic flux, A = area, θ = angle
How to Use This Calculator
1. Choose the right method
Select the formula that matches your known values. Use wire, coil, toroid, force, flux, or energy density models.
2. Enter values and units
Type the given quantities and select the matching units. The calculator automatically converts them into SI units internally.
3. Set relative permeability
Use μr = 1 for air or vacuum. Increase μr when the field exists in a magnetic material or core.
4. Calculate and review outputs
Press the calculate button. The result appears below the header and above the form, with Tesla, milliTesla, microTesla, Gauss, H, and energy density.
5. Inspect the graph
The Plotly chart visualizes how the selected model changes with distance, current, angle, radius, or energy density.
6. Export the result
Use the CSV or PDF buttons to save the current result summary for reports, lab notes, or project documentation.
Frequently Asked Questions
1. What is magnetic induction?
Magnetic induction is the magnetic flux density, usually written as B. It describes field strength and direction at a point and is commonly measured in Tesla or Gauss.
2. What is the difference between B and H?
B is magnetic flux density, while H is magnetic field intensity. They are related by B = μH, so the material permeability determines how strongly a medium responds.
3. When should I change the relative permeability value?
Keep μr at 1 for air or vacuum. Increase it when a ferromagnetic or engineered magnetic core changes the effective permeability of the medium.
4. Why does angle matter in some methods?
Force and flux formulas depend on direction. The sine or cosine term accounts for how aligned the motion, conductor, or area vector is with the magnetic field.
5. Why does the straight wire field decrease with distance?
The field spreads around the conductor in concentric circles. As radial distance increases, the same magnetic effect is distributed over a larger path.
6. Can I use negative current or negative flux values?
This calculator reports field magnitude, so it uses magnitudes for most displayed outputs. Direction conventions can be handled separately in vector analysis.
7. Which units are supported?
You can enter current, length, force, charge, velocity, flux, area, and energy density with several practical unit options. Outputs include Tesla, milliTesla, microTesla, and Gauss.
8. Are these formulas exact for every geometry?
No. Several equations assume idealized conditions, such as a long solenoid, a long straight wire, or a uniform field. Real devices can need correction factors.