Calculate current, distance, or magnetic field around a wire with Ampere’s law by entering any two values in preferred units and see steps.
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Ampere’s Law Formula
This calculator uses the magnetic field formula for a long, straight current-carrying wire. It is a common result from Ampere’s law.
- B = magnetic field strength, in teslas (T)
- I = electric current through the wire, in amperes (A)
- r = distance from the center of the wire, in meters (m)
- μ0 = permeability of free space, equal to 4π × 10-7 T·m/A
- π = pi, approximately 3.14159
If you enter current and distance, the calculator solves for the magnetic field. If you enter magnetic field and distance, it solves for current. If you enter current and magnetic field, it solves for distance from the wire. Unit selections are converted to base SI units first, then the result is converted back to the unit you selected.
Supported Unit Conversions
The formula is evaluated in amperes, meters, and teslas. These conversions are applied before and after the calculation.
| Quantity | Unit | Base-unit conversion |
|---|---|---|
| Current | mA | 1 mA = 0.001 A |
| Current | kA | 1 kA = 1000 A |
| Distance | cm | 1 cm = 0.01 m |
| Distance | mm | 1 mm = 0.001 m |
| Distance | in | 1 in = 0.0254 m |
| Distance | ft | 1 ft = 0.3048 m |
| Magnetic field | G | 1 G = 0.0001 T |
Magnetic Field Values Around a Straight Wire
| Current | Distance from wire | Magnetic field |
|---|---|---|
| 1 A | 0.1 m | 2.0 × 10-6 T |
| 5 A | 0.1 m | 1.0 × 10-5 T |
| 10 A | 0.05 m | 4.0 × 10-5 T |
| 100 A | 0.1 m | 2.0 × 10-4 T |
Example Calculations
Example 1: Find the magnetic field
Suppose a straight wire carries a current of 10 A, and you want the magnetic field 0.05 m from the wire.
The magnetic field is 0.00004 T, which is also 0.4 G.
Example 2: Find the current
Suppose the magnetic field is 0.00002 T at a distance of 0.1 m from a straight wire.
The current in the wire is 10 A.
FAQ
What form of Ampere’s law does this calculator use?
It uses the long, straight wire result: B = μ0I/(2πr). This assumes the wire is very long compared with the distance where the field is measured, and that the current is steady.
Why does the magnetic field decrease as distance increases?
For a straight wire, the magnetic field is inversely proportional to distance. If you double the distance from the wire, the magnetic field becomes half as large, assuming the current stays the same.
Can distance be zero?
No. The formula divides by distance, so r = 0 is not valid. In real wires, the field inside the conductor depends on the wire radius and current distribution, which is not handled by this calculator.