Magnetic Field Calculator - Ampere's Law

This physics calculator helps you calculate the magnetic field strength around a long straight wire carrying current using Ampere's law. The magnetic field describes the force per unit charge experienced by moving charges.

Magnetic Field Definition

• Magnetic Field: Force per unit charge per unit velocity on moving charges
• Formula: B = μ₀I/(2πr) (Magnetic Field = Permeability × Current ÷ (2π × Distance))
• Vector: Magnetic field has both magnitude and direction
• Units: Tesla (T) - SI unit of magnetic field

Magnetic Field Units

• Tesla (T): SI unit of magnetic field, 1 T = 1 N/(A⋅m)
• Millitesla (mT): 1 mT = 0.001 T
• Microtesla (μT): 1 μT = 10⁻⁶ T
• Gauss (G): 1 G = 10⁻⁴ T (CGS unit)

Ampere's Law

• Long Wire: B = μ₀I/(2πr) (field around straight wire)
• Circular Loop: B = μ₀I/(2r) (field at center)
• Solenoid: B = μ₀nI (field inside long solenoid)
• Constant: μ₀ = 4π×10⁻⁷ T⋅m/A (permeability of free space)

Applications

• Electromagnets: Magnetic field generation
• Electric Motors: Force on current-carrying wires
• Transformers: Magnetic flux and induction
• MRI Machines: Medical imaging
• Particle Accelerators: Charged particle control
• Magnetic Levitation: Transportation systems

Magnetic Field Properties

• Right-Hand Rule: Thumb in current direction, fingers show field direction
• Superposition: Total field is sum of individual fields
• No Monopoles: Magnetic field lines are always closed loops
• Gauss's Law: Net magnetic flux through closed surface is zero

Important Notes

• Magnetic field is a vector quantity
• Field strength decreases with distance from wire
• Field direction follows right-hand rule
• Field is strongest near the current-carrying wire
• Magnetic fields affect moving charges only

Magnetic Field Examples

• Long Wire: B = μ₀I/(2πr) (circular field lines)
• Circular Loop: B = μ₀I/(2r) (at center)
• Solenoid: B = μ₀nI (uniform field inside)
• Toroid: B = μ₀NI/(2πr) (field inside toroid)

Magnetic Field Effects

• Lorentz Force: F = qvB (force on moving charge)
• Magnetic Torque: τ = μB (torque on magnetic dipole)
• Magnetic Flux: Φ = BA (flux through area)
• Induction: E = -dΦ/dt (induced emf)

Safety Considerations

• High Fields: Can affect pacemakers and medical devices
• Human Safety: Fields above 5 T may be harmful
• Equipment: Magnetic fields can damage electronics
• Shielding: Ferromagnetic materials can shield fields

Magnetic Materials

• Ferromagnetic: Iron, nickel, cobalt (strong attraction)
• Paramagnetic: Aluminum, oxygen (weak attraction)
• Diamagnetic: Copper, water (weak repulsion)
• Superconductors: Perfect diamagnetism (Meissner effect)