Calculator Form
About This Magnetic Field Inside Cylinder Calculator
Fast field estimation for a cylindrical conductor
This magnetic field inside cylinder calculator estimates magnetic flux density and magnetic field intensity for a long cylindrical conductor. It follows Ampere's law. The tool accepts either total current or current density. You enter cylinder radius, radial position, and relative permeability. The calculator converts units automatically. It then reports enclosed current, H field, and B field in multiple forms. This makes quick checking easier during homework, lab review, and engineering calculations.
Why radial distance changes the result
Inside a solid cylinder with uniform current density, the magnetic field does not stay constant. It starts at zero on the centerline. It increases linearly as the observation point moves outward. This happens because a larger Amperian loop encloses more current. At the surface, the inside expression meets the outside expression. That behavior is important in electromagnetics, conductor design, and basic physics verification.
What the output tells you
The result block gives magnetic field intensity in ampere per meter and magnetic flux density in tesla, millitesla, and microtesla. It also shows total current, enclosed current, current density, radial ratio, and the formula applied. If the chosen point is outside the cylinder, the calculator switches to the outside relation automatically. This provides a clearer picture of both geometry and field behavior.
Where this calculator is useful
Students can test Ampere's law without repeating long algebra. Teachers can build worked examples quickly. Engineers can estimate local field values near cylindrical conductors, bus bars, and lab prototypes. The tool also helps when comparing total current input against current density input. Because common units are built in, conversion mistakes are reduced and repeated studies become faster.
Important assumptions behind the model
The model assumes a long solid cylinder carrying a uniformly distributed current. Edge effects are ignored. Time varying displacement current is not included. Strong non uniform material behavior is also not included. For simple design checks, education, and first pass analysis, these assumptions are often acceptable. For short conductors, layered materials, or complex geometries, use a more detailed electromagnetic model after this quick estimate.
Formula Used
This calculator uses Ampere's law for a long solid cylinder with uniform current density. Let R be cylinder radius, r be radial position, I be total current, J be current density, μ be absolute permeability, and μ = μ0μr.
- Current density from total current: J = I / (πR2)
- Enclosed current inside: Ienc = Jπr2 = I(r2/R2)
- Field intensity inside: H = Jr / 2 = I r / (2πR2)
- Flux density inside: B = μH = μJr / 2
- Field intensity outside: H = I / (2πr)
- Flux density outside: B = μI / (2πr)
The inside relation grows linearly with radius. The center field is zero. The maximum inside value occurs at the cylinder surface.
How to Use This Calculator
- Select whether you want to enter total current or current density.
- Enter the cylinder radius and choose its unit.
- Enter the radial position from the center and choose its unit.
- Enter current or current density in the selected unit.
- Enter relative permeability. Use 1 for free space or air approximation.
- Choose the number of decimal places.
- Press Calculate to show the result above the form.
- Use the CSV and PDF buttons to save the current output.
Example Data Table
| Case | Mode | Radius | Position | Input | μr | Result B |
|---|---|---|---|---|---|---|
| Example 1 | Total current | 0.05 m | 0.02 m | 10 A | 1 | 0.000016 T |
| Example 2 | Current density | 0.10 m | 0.04 m | 2000 A/m2 | 1 | 0.00005027 T |
| Example 3 | Total current | 0.03 m | 0.05 m | 25 A | 1 | 0.0001 T |
FAQs
1. What formula is used inside the cylinder?
For a solid cylinder with uniform current density, the calculator uses H = Jr/2 and B = μJr/2. If total current is entered, it uses the equivalent form H = I r / (2πR2).
2. Does this calculator work for a hollow cylinder?
No. This version assumes a solid cylinder with uniform current distribution. A hollow cylinder needs a different enclosed current relation and possibly different assumptions about current placement.
3. Why does the field increase linearly inside?
The enclosed current grows with the area of the Amperian loop. Because that area depends on r2, the final inside field becomes proportional to r for uniform current density.
4. What happens if the radial position is larger than the radius?
The calculator automatically switches to the outside cylinder expression. It still reports a valid result, but the status line tells you that the selected point is outside the conductor.
5. What does relative permeability mean here?
Relative permeability scales the magnetic response of the medium. Use 1 for air or free space approximation. Larger values increase the flux density B for the same magnetic field intensity H.
6. Should I enter total current or current density?
Use total current when you know the complete conductor current. Use current density when the problem gives current per unit area. The calculator can convert either input path into the same physical result.
7. Are time varying effects included?
No. This is a steady current model based on Ampere's law. It does not include displacement current, wave effects, or detailed transient electromagnetic behavior.
8. Can I save the result for records?
Yes. After calculation, use the CSV button for tabular data or the PDF button for a quick report of the displayed result.