Calculator Inputs
Use a direct surface current density or compute it from total current and sheet width. The page stays single column, while the form fields use a responsive grid.
Plotly Graph
This graph shows the signed field component across the sheet. The discontinuity at the sheet is expected for an ideal current sheet.
Formula Used
Magnitude from Ampère’s law:
∮ B · dl = μIenc
2BL = μKL
B = μK / 2
For an ideal infinite sheet in the xy plane, the magnetic field magnitude is constant on each side. It depends on permeability μ and surface current density K, not on the size of the distance from the sheet.
Vector form: For the side above the sheet, B⃗(d > 0) = (μ/2)(K⃗ × ẑ). For the side below the sheet, B⃗(d < 0) = −(μ/2)(K⃗ × ẑ).
When K comes from total current: K = I / w, where I is total current and w is the effective sheet width.
How to Use This Calculator
- Select whether you want to enter surface current density directly or compute it from total current and width.
- Enter relative permeability μr for the medium. Use 1 for free space or air.
- Enter distance d. Positive values mean above the sheet, negative values mean below it.
- Choose the current direction within the sheet plane.
- Set the graph half-range, then press Calculate Magnetic Field.
- Review the result card, vector direction, expressions, graph, and export buttons.
Expression for B⃗(d) Above the xy Plane
If the sheet lies in the xy plane and carries a uniform surface current density K⃗, then for points above the plane:
B⃗(d > 0) = (μ/2)(K⃗ × ẑ)
For example, if K⃗ = Kx̂, then B⃗(d > 0) = −(μK/2)ŷ. Below the plane, the direction reverses.
Example Data Table
These examples assume an ideal infinite sheet. Magnitude stays unchanged when only the sign of d changes.
| Case | K (A/m) | μr | d (m) | Direction | |B| (T) | Field Vector |
|---|---|---|---|---|---|---|
| 1 | 2.000000 | 1.00 | 0.15 | +x̂ | 0.000001257 | −ŷ |
| 2 | 5.000000 | 1.00 | -0.40 | +x̂ | 0.000003142 | +ŷ |
| 3 | 10.000000 | 2.00 | 0.25 | +ŷ | 0.000012566 | +x̂ |
| 4 | 20.000000 | 1.50 | -0.80 | −ŷ | 0.000018850 | +x̂ |
FAQs
1. What does this calculator compute?
It computes the magnetic field created by an ideal uniform sheet of current. It reports magnitude, field direction, side of the sheet, unit conversions, a graph, and exportable results.
2. Which formula is used?
The calculator uses Ampère’s law. For an infinite current sheet, the field magnitude is B = μK/2. If you enter total current and width, it first calculates K = I/w.
3. Why does the magnitude not change with distance?
For an ideal infinite sheet, symmetry makes the field strength constant on each side. Moving farther away changes neither enclosed current per unit length nor the resulting field magnitude.
4. Write an expression for B⃗(d), the magnetic field above the xy plane.
For a sheet in the xy plane carrying surface current density K⃗, the field above it is B⃗(d > 0) = (μ/2)(K⃗ × ẑ). If K⃗ = Kx̂, then B⃗(d > 0) = −(μK/2)ŷ.
5. What happens exactly at d = 0?
The ideal sheet creates a discontinuity in field direction across the surface. At d = 0, many texts use the average field value, which is zero, unless boundary conditions specify otherwise.
6. Can I enter total current instead of surface current density?
Yes. Choose the current-and-width mode. The calculator converts your values using K = I/w, then uses the same magnetic-field formula for the final result.
7. Why can I change relative permeability?
Relative permeability lets you model media other than vacuum. The total permeability is μ = μ0μr, so magnetic materials can increase the field magnitude compared with free space.
8. What units are included in the result?
The result is displayed in tesla, millitesla, microtesla, and gauss. That makes it easier to compare values used in classroom problems, engineering calculations, and practical magnetic-field estimates.