An abampere (often written as ab ampere) is the fundamental unit of electric current in the electromagnetic centimeter-gram-second (emu-cgs) system, equal to exactly 10 standard SI amperes. If you are reading older physics literature, restoring vintage magnetics equipment, or working with Gaussian units for magnetic fields, you will encounter this unit. Failing to convert it properly will throw your calculations off by a full order of magnitude, potentially leading to saturated transformer cores or blown fuses on the bench.
The Core Definition and the Unit Conversion Table
Before the global adoption of the Système International (SI) in the mid-20th century, physicists and engineers relied heavily on the CGS system. The CGS system actually split into two distinct subsystems for electromagnetism: the electrostatic system (esu) and the electromagnetic system (emu). The abampere is the base current unit of the emu-cgs system. It is defined as the constant current that, flowing in a circular arc of 1 centimeter radius and 1 centimeter length, produces a magnetic field of 1 oersted at the center of the arc.
Because the emu-cgs system was built around magnetic phenomena rather than static charges, its base units are scaled very differently from the SI system we use on modern digital multimeters. The table below maps the abampere against the units you are most likely to confuse it with.
| Unit Name | System | Symbol | Equivalent in SI Amperes | Common Use Case |
|---|---|---|---|---|
| Abampere (or Biot) | CGS-emu | abA, Bi | 10 A (exact) | Legacy magnetics, older physics texts, Gaussian unit conversions |
| Ampere | SI (Modern) | A | 1 A (exact) | All modern electrical engineering, NEC wiring, bench measurements |
| Statampere | CGS-esu | statA, Fr/s | ~3.3356 × 10-10 A | Electrostatics, capacitor theory in older literature |
| Milliampere | SI (Submultiple) | mA | 0.001 A (exact) | Microcontrollers, ESP32 GPIO limits, sensor outputs |
| Gilbert (Current equiv) | CGS-emu (MMF) | Gb | 10 / (4π) A (approx 0.795 A) | Magnetomotive force in legacy magnetic circuit design |
Worked Numeric Example: Solenoid Magnetic Field Calculation
To understand why this unit matters, we need to look at what it changes in a real calculation. In a physical circuit, an abampere changes absolutely nothing; electrons do not care which unit system you use to count them. However, in a design installation or calculation workflow, using abamperes changes the constants in your formulas. Specifically, the permeability of free space (μ0) disappears from CGS-emu equations, replaced by a simple geometric factor of 4π.
Let’s calculate the magnetic field inside a solenoid using both systems to prove the math aligns when conversions are handled correctly.
The Setup
- Coil Length: 10 cm (0.1 meters)
- Total Turns: 500
- Turn Density (n): 50 turns/cm (or 5,000 turns/m)
- Applied Current: 2 standard Amperes
Method 1: Standard SI Calculation
In SI units, the magnetic field (B) in Tesla is calculated as:
B = μ₀ × n × I
Where μ₀ = 4π × 10-7 T·m/A.
B = (4π × 10⁻⁷) × 5000 × 2
B = 40,000π × 10⁻⁷ = 0.004π Tesla
B ≈ 0.012566 Tesla (or 12.566 mT)
Method 2: CGS-emu Calculation (Using Abamperes)
In the emu-cgs system, the formula for a solenoid's magnetic field (B) in Gauss simplifies because the medium's permeability is dimensionless and defaults to 1 in a vacuum:
B = 4π × n × I_ab
First, we must convert our 2 SI Amperes into abamperes. Since 1 abampere = 10 A, we divide by 10:
I_ab = 2 A / 10 = 0.2 abamperes
Now, plug the values into the CGS formula (remember, n must be in turns/cm for CGS):
B = 4π × 50 × 0.2
B = 40π Gauss
B ≈ 125.66 Gauss
Verification
Since 1 Tesla equals exactly 10,000 Gauss, we convert our SI result:
0.012566 T × 10,000 = 125.66 Gauss.
The math matches perfectly. If you had forgotten to convert the 2 Amperes into 0.2 abamperes and plugged '2' directly into the CGS formula, you would have calculated 400π Gauss (1,256 Gauss), overestimating your magnetic field by a factor of 10. In a real magnetics design, this error would lead you to select a core material that saturates immediately under load.
Where You Meet the Ab Ampere in Practice
You will rarely, if ever, see an abampere on a modern commercial schematic, a breaker panel label, or an Arduino datasheet. The NIST and BIPM have thoroughly standardized the SI Ampere for all modern engineering. However, you will meet the abampere in three specific scenarios:
- Legacy Magnetics and Transformer Design: If you are repairing or reverse-engineering aerospace or military hardware from the 1950s and 60s, the original design documents often use CGS-emu units. Core loss charts and B-H curves in these manuals plot flux density in Gauss and magnetizing force in Oersteds, which inherently assumes current is being calculated in abamperes or Gilberts.
- Advanced Physics and Astrophysics: Many subfields of plasma physics and astrophysics still use Gaussian units (a hybrid of esu and emu) because it simplifies Maxwell's equations by eliminating ε₀ and μ₀. When reading papers on magnetic confinement fusion or stellar magnetic fields, current densities are frequently expressed in abamperes per square centimeter.
- The Biot-Savart Law in Textbooks: Older editions of classic texts, such as Panofsky and Phillips' Classical Electricity and Magnetism, derive the Biot-Savart law using emu-cgs. If you are a student or hobbyist working through these derivations to build a custom Helmholtz coil, you must track the abampere to avoid scaling errors.
Common Confusions: Abamperes, Statamperes, and Amperes
What do people commonly confuse the abampere with?
The most common confusion is between the abampere (electromagnetic CGS) and the statampere (electrostatic CGS). Because both are 'CGS units of current', readers assume they are interchangeable. They are not. A statampere is incredibly small (about 0.33 nanoamperes), while an abampere is quite large (10 Amperes). The HyperPhysics unit conversion database clearly delineates these two distinct CGS branches. Mixing them up introduces an error factor related to the speed of light (c ≈ 3 × 10¹⁰ cm/s).
Is an abampere the same as a 'deciampere' or 'dekaampere'?
No. While 1 abampere happens to equal 10 Amperes (which is technically 1 dekaampere in SI prefix terminology), the abampere is a base unit of an entirely different measurement system, not an SI prefixed unit. You will never see 'daA' used in place of 'abA' in physics literature.
Does the NEC or local electrical code recognize the abampere?
Absolutely not. The National Electrical Code (NEC), IEC standards, and all local Authorities Having Jurisdiction (AHJ) strictly use the SI Ampere for wire ampacity, breaker sizing, and load calculations. If you are sizing a breaker for a 15 A branch circuit, you are using SI Amperes. Never attempt to submit permit drawings or load calculations using CGS units.
Why did the industry abandon the abampere?
The CGS-emu system was highly elegant for theoretical physics but terrible for practical engineering. Because the base units (abampere, abvolt, abohm) resulted in incredibly large or incredibly small numbers for everyday electrical work, engineers had to constantly use 'practical units' (Amperes, Volts, Ohms) alongside theoretical formulas. The adoption of the SI system unified the theoretical and practical units into a single, coherent framework, rendering the abampere obsolete for daily use.
