Magnetic Field Calculator

Calculate magnetic field strength from current in wires, solenoids, and current loops. Essential for electromagnetism, motor design, and physics applications.

**Long Straight Wire:** B = μ₀ × I / (2πr) Where: • B = Magnetic field (T) • μ₀ = Permeability of free space = 4π×10⁻⁷ T·m/A • I = Current (A) • r = Perpendicular distance from wire (m) **Solenoid (Inside):** B = μ₀ × n × I = μ₀ × N × I / L Where: • n = Turn density (turns per meter) • N = Total number of turns • L = Solenoid length (m) **Solenoid End:** B_end = μ₀ × n × I / 2 **Current Loop Center:** B = μ₀ × N × I / (2R) Where: • N = Number of loops • R = Loop radius (m) **Unit Conversions:** • 1 T (Tesla) = 10,000 G (Gauss) • 1 T = 1000 mT (millitesla) • 1 T = 10⁶ μT (microtesla) **Right-Hand Rule:** Wire: Thumb = current, fingers = field circles Solenoid: Fingers = current through loops, thumb = field direction
**Example 1 (Household Wire):** Current = 10 A, Distance = 5 cm = 0.05 m • B = 4π×10⁻⁷ × 10 / (2π × 0.05) • B = 4×10⁻⁵ T = 40 μT = 0.4 Gauss (Safe level, similar to Earth's field) **Example 2 (Power Line):** Current = 1000 A, Distance = 10 m • B = 4π×10⁻⁷ × 1000 / (2π × 10) • B = 2×10⁻⁵ T = 20 μT = 0.2 Gauss **Example 3 (Solenoid with Turn Density):** Current = 2 A, Turn density = 1000 turns/m • B = 4π×10⁻⁷ × 1000 × 2 • B = 2.51×10⁻³ T = 2.51 mT = 25.1 Gauss **Example 4 (Solenoid with Total Turns):** Current = 5 A, Total turns = 500, Length = 0.25 m • n = 500 / 0.25 = 2000 turns/m • B = 4π×10⁻⁷ × 2000 × 5 • B = 1.26×10⁻² T = 12.6 mT = 126 Gauss • B_end = 6.3 mT (at solenoid face) **Example 5 (Single Current Loop):** Current = 3 A, Radius = 0.1 m, Loops = 1 • B = 4π×10⁻⁷ × 1 × 3 / (2 × 0.1) • B = 1.88×10⁻⁵ T = 18.8 μT = 0.188 Gauss **Example 6 (Multi-turn Coil):** Current = 1 A, Radius = 0.05 m, Loops = 100 • B = 4π×10⁻⁷ × 100 × 1 / (2 × 0.05) • B = 1.26×10⁻³ T = 1.26 mT = 12.6 Gauss **Example 7 (MRI-like Solenoid):** Current = 100 A, Turn density = 10,000 turns/m • B = 4π×10⁻⁷ × 10,000 × 100 • B = 1.26 T = 1260 mT (strong field!) **Example 8 (Wire at 1 cm):** Current = 15 A, Distance = 0.01 m • B = 4π×10⁻⁷ × 15 / (2π × 0.01) • B = 3×10⁻⁴ T = 0.3 mT = 3 Gauss

What is a magnetic field?

A magnetic field is a region where magnetic forces act on moving charges and magnetic materials. Field strength B (measured in Tesla or Gauss) indicates the force on a moving charge or current-carrying wire. Magnetic fields are produced by moving charges and intrinsic magnetic moments.

What is the formula for magnetic field around a wire?

For a long straight wire carrying current I, the magnetic field at distance r is B = μ₀I/(2πr), where μ₀ = 4π×10⁻⁷ T·m/A is the permeability of free space. The field forms circular loops around the wire (right-hand rule).

How do I calculate the magnetic field of a solenoid?

Inside a long solenoid with n turns per meter carrying current I, the field is uniform: B = μ₀nI. For N total turns over length L: B = μ₀NI/L. Outside an ideal solenoid, the field is nearly zero.

What is the difference between Tesla and Gauss?

Tesla (T) and Gauss (G) both measure magnetic field strength. 1 Tesla = 10,000 Gauss. Tesla is the SI unit, used for strong fields (MRI: 1-3 T). Gauss is convenient for weaker fields (Earth: ~0.5 G, refrigerator magnet: ~100 G).

What is magnetic permeability μ₀?

Magnetic permeability of free space μ₀ = 4π×10⁻⁷ T·m/A (or H/m) relates magnetic field to current. In materials, relative permeability μᵣ modifies this: B = μ₀μᵣH. Ferromagnetic materials (iron) have μᵣ >> 1.

How does the right-hand rule work for magnetic fields?

For a straight wire: point your right thumb in the current direction; fingers curl in the field direction. For a solenoid: curl fingers in current direction through loops; thumb points to north pole (field direction inside).

What is the magnetic field in a current loop?

At the center of a circular loop of radius R carrying current I: B = μ₀I/(2R). For N loops: B = μ₀NI/(2R). The field is strongest at the center and weakens with distance along the axis.

How strong are typical magnetic fields?

Earth's field: ~50 μT (0.5 G), Refrigerator magnet: ~5 mT (50 G), MRI machine: 1-3 T (10,000-30,000 G), Sunspot: 0.3 T, Neutron star: 10⁸ T, Large Hadron Collider magnets: 8 T, Strong lab magnets: up to 45 T.

What is the force on a current-carrying wire in a magnetic field?

The force is F = BIL sin(θ), where B is field strength, I is current, L is wire length in the field, and θ is the angle between field and current. Maximum force occurs when perpendicular (θ = 90°).

Can magnetic fields do work on charged particles?

No! Magnetic force is always perpendicular to velocity (F = qv×B), so it can't change kinetic energy, only direction. This is why particles move in circles in uniform magnetic fields. Electric fields do work and change energy.

What is the difference between B and H fields?

B (magnetic flux density, in Tesla) is the total field including material effects. H (magnetic field intensity, in A/m) is the field from currents alone. In vacuum: B = μ₀H. In materials: B = μ₀μᵣH. B is what forces act on; H is what currents create.

How do I calculate the field at the end of a solenoid?

At the end face of a semi-infinite solenoid, the field is exactly half the interior value: B = μ₀nI/2. This is because the field lines spread out from one end, rather than being confined inside the solenoid.

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