ELECTROMAGNETISMElectricityPhysics Calculator
🧲

Magnetic Field of Straight Wire

A current I in a straight wire produces a magnetic field B = μ₀I/(2πr) at distance r, circling the wire (right-hand rule). Ampère's law: ∮B·dl = μ₀I_enc. Finite wire: B = (μ₀I/4πr)(cos θ₁ − cos θ₂).

Did our AI summary help? Let us know.

B = μ₀I/(2πr) for infinite straight wire; circles wire. μ₀ = 4π×10⁻⁷ T·m/A (permeability of free space). 1 A at 1 cm: B ≈ 20 μT (0.2 G). Parallel wires: force per length F/L = μ₀I₁I₂/(2πd).

Key quantities
B = μ₀I/(2πr)
Infinite wire
Key relation
B = (μ₀I/4πr)(cos θ₁−cos θ₂)
Finite wire
Key relation
∮B·dl = μ₀I_enc
Ampère's law
Key relation
Right-hand rule: thumb = I
Direction
Key relation

Ready to run the numbers?

Why: Magnetic fields from wires underlie motors, transformers, and transmission lines. Biot-Savart and Ampère's law are fundamental to electromagnetism.

How: Infinite wire: B ∝ I/r, azimuthal. Finite wire uses angles from ends. Ampère's law for symmetric geometries. Parallel wires attract/repel via B from each.

B = μ₀I/(2πr) for infinite straight wire; circles wire.μ₀ = 4π×10⁻⁷ T·m/A (permeability of free space).
Sources:NIST Physical ConstantsHyperPhysics - Biot-Savart Law

Run the calculator when you are ready.

Calculate Magnetic FieldEnter current and distance for B

⚡ Power Transmission Line

High-voltage power line: I=1000 A, r=50 m

🔌 Parallel Bus Bars

Electrical bus bars: I₁=500 A, I₂=500 A, d=0.1 m, L=2 m

📡 Coaxial Cable

Coaxial cable inner conductor: I=5 A, r=0.01 m

🧲 Electromagnet Coil

Solenoid coil: I=10 A, N=1000 turns, r=0.05 m

🏠 Household Wiring

Home electrical wire: I=15 A, r=0.02 m

📏 Finite Wire Segment

Finite wire: I=20 A, L=1 m, r=0.1 m, θ₁=30°, θ₂=150°

Input Parameters

❓ Frequently Asked Questions

What is the magnetic field around a straight wire?

When electric current flows through a straight wire, it generates a circular magnetic field around the wire. The field strength decreases with distance from the wire and is proportional to the current magnitude. The direction follows the right-hand rule: point your thumb in the current direction, and your curled fingers show the field direction.

How does distance affect magnetic field strength?

The magnetic field strength is inversely proportional to the distance from the wire. For an infinite wire, B = μ₀I/(2πr), meaning doubling the distance halves the field strength. This inverse relationship is fundamental to magnetic field calculations.

What is the difference between infinite and finite wire calculations?

An infinite wire assumes the wire extends infinitely in both directions, simplifying to B = μ₀I/(2πr). A finite wire accounts for the wire ends using angles θ₁ and θ₂: B = (μ₀I/4πr)(cos θ₁ - cos θ₂). Finite wire calculations are more accurate for real-world applications.

How do parallel wires interact magnetically?

Two parallel current-carrying wires experience a force due to their magnetic fields. The force per unit length is F/L = μ₀I₁I₂/(2πd). Wires with currents in the same direction attract each other, while opposite-direction currents repel. This principle is used in electromagnets and motor design.

What is Ampère's law and when is it used?

Ampère's law states that the line integral of the magnetic field around a closed loop equals μ₀ times the current enclosed: ∮B·dl = μ₀I_enclosed. It's particularly useful for calculating magnetic fields with high symmetry, such as infinite wires, solenoids, and toroids.

What are safe magnetic field levels?

Earth's magnetic field is about 50 μT (0.00005 T). MRI machines operate at 1-3 T. Fields above 0.01 T (10 mT) can affect electronic devices and pacemakers. Occupational exposure limits are typically 0.5 T for whole-body exposure. Always consult safety guidelines for specific applications.

How do I convert between tesla, gauss, and other units?

1 tesla (T) = 10,000 gauss (G) = 1,000,000 microtesla (μT). The tesla is the SI unit, while gauss is commonly used in older literature. For reference: Earth's field ≈ 50 μT, refrigerator magnet ≈ 0.01 T, MRI ≈ 1-3 T.

Can I calculate the magnetic field for non-straight wires?

Yes, but it requires more complex calculations. For curved wires, loops, or coils, you use the Biot-Savart law or Ampère's law with appropriate symmetry. This calculator focuses on straight wires, but the principles extend to other geometries.

📚 Official Data Sources

NIST Physical Constants

Fundamental physical constants database

https://physics.nist.gov/cuu/Constants/

Last updated: 2026-02-01

Griffiths - Introduction to Electrodynamics

Standard electromagnetism textbook (4th Edition)

https://www.pearson.com/

Last updated: 2017-01-01

HyperPhysics - Biot-Savart Law

Educational resource on magnetic fields from currents

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

Last updated: 2026-02-06

Physics LibreTexts - Ampère's Law

Open educational resource for physics

https://phys.libretexts.org/

Last updated: 2026-02-06

Jackson - Classical Electrodynamics

Advanced electromagnetism reference (3rd Edition)

https://www.wiley.com/

Last updated: 1998-01-01

⚠️ Disclaimer

This calculator provides magnetic field calculations based on standard electromagnetic theory and physical constants. Results are approximations and may vary based on:

  • Wire geometry assumptions (infinite vs finite wire approximations)
  • Precision of input values and rounding in calculations
  • Environmental factors affecting magnetic field propagation
  • Material properties and proximity effects not accounted for in ideal calculations

This tool is for educational and general reference purposes only. For critical applications involving magnetic fields (medical devices, electronic systems, safety assessments), consult professional engineering standards, account for real-world conditions, and consider safety regulations regarding magnetic field exposure.

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

🧲

Biot-Savart law gives B from current elements; Ampère's law for symmetric cases.

— Griffiths

📐

Field lines circle the wire; direction by right-hand rule.

— Electromagnetism

⚡

Household wire: 10 A at 1 cm gives B ~ 0.2 mT (Earth's B ~ 50 μT).

— Practical values

🔄

Two parallel currents: same direction attract; opposite repel.

— Force between wires

What is Magnetic Field of a Straight Wire?

The magnetic field around a straight current-carrying wire is a fundamental concept in electromagnetism. When electric current flows through a conductor, it generates a circular magnetic field around the wire. The strength of this field depends on the current magnitude and the distance from the wire.

🔬 Key Concepts

Right-Hand Rule

Point your right thumb in the direction of current flow. Your curled fingers show the direction of the magnetic field lines circling the wire.

Field Strength

The magnetic field strength decreases inversely with distance from the wire. Doubling the distance halves the field strength.

Field Direction

The magnetic field forms concentric circles around the wire, perpendicular to both the wire and the radial direction.

Current Dependence

The field strength is directly proportional to the current. Doubling the current doubles the magnetic field strength.

💡 Important Note

The magnetic field around a straight wire follows the Biot-Savart law for finite wires and simplifies to Ampère's law for infinite wires. The field strength is measured in tesla (T) or gauss (G), where 1 T = 10,000 G.

How to Calculate Magnetic Field

Calculating the magnetic field around a straight wire involves different formulas depending on whether the wire is infinite, finite, or part of a parallel wire system. Here's how to approach each scenario:

Infinite Wire Method

  1. 1Identify the current (I) in amperes flowing through the wire
  2. 2Measure the perpendicular distance (r) from the wire to the point of interest
  3. 3Apply the formula: B = μ₀I/(2πr) where μ₀ = 4π × 10⁻⁷ T·m/A
  4. 4Convert units if needed: 1 T = 10,000 G = 1,000,000 μT

Finite Wire Method

  • Determine the angles θ₁ and θ₂ from the wire ends to the point of interest
  • Measure the perpendicular distance from the wire to the point
  • Apply: B = (μ₀I/4πr)(cos θ₁ - cos θ₂)
  • For a semi-infinite wire, one angle is 90° and the other is 0° or 180°

Parallel Wires Force Method

  • Identify currents I₁ and I₂ in both wires
  • Measure the separation distance d between the wires
  • Calculate force per length: F/L = μ₀I₁I₂/(2πd)
  • Determine force direction: attractive for same-direction currents, repulsive for opposite

When to Use Magnetic Field Calculator

Magnetic field calculations for straight wires are essential in electrical engineering, physics research, and practical applications involving current-carrying conductors. Understanding when and how to apply these calculations is crucial for proper system design and safety.

Power Transmission

Calculate magnetic fields around high-voltage power lines to assess environmental impact and ensure safe distances from sensitive equipment.

Applications:

  • Power line field assessment
  • EMI interference analysis
  • Safety distance calculations

Circuit Design

Design electrical circuits and bus bars with proper spacing to minimize magnetic interference and calculate forces between parallel conductors.

Benefits:

  • Bus bar design
  • Force calculations
  • EMI reduction

Physics Education

Teach electromagnetism concepts, demonstrate Ampère's law applications, and visualize magnetic field patterns around conductors.

Educational Use:

  • Concept visualization
  • Problem solving
  • Lab calculations

Magnetic Field Calculation Formulas

Understanding magnetic field formulas is essential for electromagnetism calculations. These formulas relate magnetic field strength to current, distance, and geometry of the conductor.

📊 Core Magnetic Field Formulas

Infinite Wire Magnetic Field

B=fracmu0I2pirB = \\frac{\\mu_0 I}{2\\pi r}

Magnetic field around an infinitely long straight wire, where μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space, I is the current, and r is the distance from the wire.

Finite Wire Magnetic Field

B=fracmu0I4pir(costheta1−costheta2)B = \\frac{\\mu_0 I}{4\\pi r}(\\cos \\theta_1 - \\cos \\theta_2)

Magnetic field from a finite straight wire segment, where θ₁ and θ₂ are angles from the wire ends to the point of interest.

Force Between Parallel Wires

fracFL=fracmu0I1I22pid\\frac{F}{L} = \\frac{\\mu_0 I_1 I_2}{2\\pi d}

Force per unit length between two parallel current-carrying wires separated by distance d. Wires attract if currents are in the same direction, repel if opposite.

Ampère's Law

ointmathbfBcdotdmathbfl=mu0Itextenclosed\\oint \\mathbf{B} \\cdot d\\mathbf{l} = \\mu_0 I_{\\text{enclosed}}

Ampère's circuital law states that the line integral of magnetic field around a closed loop equals μ₀ times the current enclosed by the loop.

Permeability of Free Space

mu0=4pitimes10−7textT⋅m/A=1.25663706212times10−6textT⋅m/A\\mu_0 = 4\\pi \\times 10^{-7} \\text{ T \cdot m/A} = 1.25663706212 \\times 10^{-6} \\text{ T \cdot m/A}

Fundamental constant relating magnetic field to current in vacuum. This constant appears in all magnetic field calculations.

HI THERE
👋Magnetic fields from wires underlie motors, transformers, and transmission lines.
AI
NumberVibe

Related Calculators

Magnetic Force on Current-Carrying Wire Calculator

Calculate magnetic force on current-carrying wires using F = BIL sin(θ), torque on current loops (τ = NBIA sin(θ)), motor force calculations, and...

Physics

Magnetic Force Between Current-Carrying Wires Calculator

Calculate the magnetic force between parallel current-carrying wires, including force per unit length (F/L = μ₀I₁I₂/(2πd)), total force for given wire...

Physics

AC Wattage Calculator

Comprehensive AC power calculator for single-phase and three-phase systems with real power, apparent power, reactive power, power factor analysis, and power...

Physics

Boost Converter Calculator

Calculate boost converter (step-up) parameters including duty cycle, output voltage (Vout = Vin/(1-D)), inductor and capacitor selection, current/voltage...

Physics

Breaker Size Calculator

Calculate proper circuit breaker sizing for electrical loads. Supports single-phase and three-phase systems, continuous/non-continuous loads, motor circuits...

Physics

Bridge Rectifier Calculator

Calculate bridge rectifier DC output voltage, peak inverse voltage (PIV), ripple voltage, filter capacitor sizing, diode current ratings, and power...

Physics