Linear Current Density & Solenoid B-Field Calculator

Magnetostatics, Ampere's Law & Linear Current Density Metrology

Linear Current Density represents the electric current per unit transverse width flowing across a 2D surface sheet:

• **

• Universal Linear Current Conversion Formulas (SI Standards)**:

1 A/cm = 100 A/m = 0.10 A/mm = 2.54 A/in

1 A/in = 39.3701 A/m = 0.393701 A/cm

1 Oersted (Oe) = (1,000) / (4π) A/m = 79.57747 A/m

1 abA/cm = 1,000 A/m

• **

• Ampere's Law for Solenoids & Current Sheets**:

B · dl = μ_0 I_enc B = μ_r μ_0 K = μ_r μ_0 (n × I) (Tesla, T)

I_total = K × w (Total Current in Amperes)

Δ B = μ_0 K (Magnetic Field Discontinuity across Surface Current Sheet)

• **

• Standard Electrodynamic & Magnetic Benchmarks**:

• PCB Ground Plane Return: 10.0 A/m 0.10 A/cm B = 12.57 µT

• Lab Air-Core Solenoid: 1,000.0 A/m 10.0 A/cm B = 1.257 mT (12.57 G)

• Induction Heating Coil: 50,000.0 A/m = 500.0 A/cm B = 62.83 mT

• Superconducting MRI Magnet: 100,000.0 A/m = 1,000.0 A/cm B = 0.1257 Tesla

How to Use This Calculator

Enter your Linear Current Density (K = I/w) (e.g. 1000 in K), From Linear Current Density Unit — choose from Amperes per Meter (A/m - SI Base Unit), Amperes per Centimeter (A/cm = 100 A/m - Solenoids), Amperes per Millimeter (A/mm = 1,000 A/m), To Linear Current Density Unit — choose from Amperes per Centimeter (A/cm), Amperes per Meter (A/m), Amperes per Millimeter (A/mm), Conductor Sheet Width / Solenoid Length (w in meters) (e.g. 0.50 in m), Core Relative Permeability (µ_r, 1.0 = Air/Vacuum) (e.g. 1.0 in µ_r), and Electrodynamic & Magnet Benchmark — choose from Custom Linear Current Sheet, Laboratory Air-Core Solenoid (1,000.0 A/m) → 10.0 A/cm | Total I = 500 A (0.5m) | B = 1.257 mT (12.57 Gauss), Superconducting MRI Magnet Winding (100.0 kA/m = 1,000 A/cm) → 100,000 A/m | B = 0.1257 Tesla (Air core). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Total Current: I = K * w (in Amperes)

Ampere's Law Magnetic Field: B = mu_r mu_0 K (in Tesla -> mT and Gauss)

Worked Example

An electrical engineer building an air-core solenoid coil wound with turn density n = 1,000 turns/meter carrying I = 1.0 Amp calculates the linear current density is K = 1,000 A/m, producing an internal magnetic field B = μ_0 K = 1.257 mT (12.57 Gauss).

Understanding Your Result

Housing affordability benchmarks: keep total housing costs (rent or mortgage + utilities + insurance) below 30% of gross income. The "28/36 rule" for mortgages: housing costs ≤28% and total debt ≤36% of gross monthly income. In high-cost metros (NYC, SF, LA), many residents spend 35–50% of income on housing — financial planners recommend aggressive savings to compensate when above 30%. Every 100/month increase in housing cost reduces your sustainable savings rate by approximately 2% of average US income.