Magnetism studies magnetic fields and forces. Magnetic field B (Tesla) is produced by currents. Force on wire: F = ILB sin θ. Torque on loop: τ = mB sin θ. Magnetic flux: Φ = BA cos θ. Magnetic moment: m = IA. Cyclotron: r = mv/(qB), f = qB/(2πm).
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Field, force, torque, flux, moment, cyclotron
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| Concept | Formula | Notes / Units / Conditions |
|---|---|---|
| Magnetic field (wire) | B = μ₀ I / (2 π r) | At perpendicular distance r |
| Magnetic field (loop center) | B = μ₀ I / (2 R) | At center of circular loop |
| Magnetic field (solenoid) | B = μ₀ n I | n = turns per unit length |
| Force on wire | F = I L B sin θ | L = length vector |
| Torque on loop | τ = m B sin θ | m = I A (magnetic moment) |
| Magnetic flux | Φ = B A cos θ | Weber (Wb = T·m²) |
| Magnetic moment | m = I A | A·m², direction by right-hand rule |
| Cyclotron radius | r = m v / (q B) | Charged particle in B field |
| Cyclotron frequency | f = q B / (2 π m) | Independent of velocity |
| Force between wires | F/L = μ₀ I₁ I₂ / (2 π d) | Definition of 1 ampere |
About Magnetism
Magnetism studies magnetic fields and forces. Magnetic field B (Tesla) is produced by electric currents. Force on current-carrying wire: F = ILB sin θ. Torque on magnetic dipole: τ = mB sin θ. Magnetic flux: Φ = BA cos θ.
Magnetic Field
Magnetic field B (Tesla = N/(A·m) = Wb/m²) is force per unit charge-velocity. For straight wire: B = μ₀I/(2πr). For circular loop center: B = μ₀I/(2R). For solenoid: B = μ₀nI, where n is turns per unit length. μ₀ = 4π × 10⁻⁷ T·m/A.
Force and Torque
Force on wire: F = ILB sin θ, where I is current, L is length vector, B is magnetic field, θ is angle. Direction: right-hand rule. Torque on loop: τ = mB sin θ, where m = IA is magnetic moment. Tends to align with field.
Magnetic Flux and Moment
Magnetic flux Φ = B·A = BA cos θ (Weber = T·m²). Scalar quantity. For coil: NΦ (linked flux). Faraday's law: EMF = -dΦ/dt. Magnetic moment m = IA (A·m²) for current loop. Direction perpendicular to plane (right-hand rule).
Cyclotron Motion
Cyclotron radius: r = mv/(qB) for charged particle in magnetic field. Cyclotron frequency: f = qB/(2πm), independent of velocity. Used in particle accelerators and mass spectrometers.