Applied Connections — Technology and Engineering Applications of MAG-01 — Summary

MRI Scanners: Superconducting solenoids create 1.5–3 T uniform field; principle B = μ_{0}nI with very high n; superconducting wire eliminates resistance, allowing enormous sustained currents; the uniform field inside the long bore is the Solenoid principle applied at hospital scale
Electric Motors: Convert electrical energy to mechanical energy via τ = NIAB; rotating coil in permanent magnet field; commutator reverses current direction every half turn to maintain unidirectional torque; efficiency determined by N, A, B, and current I
Loudspeakers: Current-carrying voice coil in radial magnetic field; F = BIl → force proportional to audio current → drives cone → sound; linear relationship between current and force gives low distortion
Cyclotron (Particle Accelerator): Uses f = $\frac{qB}{2πm}$ — constant frequency irrespective of particle speed; protons are accelerated repeatedly at the gap between D-shaped electrodes; radius increases with speed (r = $\frac{mv}{qB}$ ) but period stays constant; used in cancer proton therapy and fundamental physics
Mass Spectrometer: Different isotopes have different masses → r = $\frac{mv}{qB}$ → different radii → separated on photographic plate; velocity selector (E = vB) pre-selects particles before injection
Hard Disk Drive: Ferromagnetic domain orientations encode binary data; high-coercivity material (hard ferromagnet) resists accidental demagnetisation; read head detects fringe field of domains; areal density limited by superparamagnetism at very small domain sizes
Transformer Core: Soft iron (high μᵣ, low coercivity) concentrates flux; laminated sheets break eddy current paths; hysteresis loop area minimised (soft material) to reduce core losses; core loss = loop area × frequency
Magnetic Levitation (Maglev Trains): Diamagnetic levitation (Meissner effect in superconductors, extreme case of χ = −1); induced currents create repulsive force; train "floats" without contact → zero friction → high speed
Geophysical Compasses: Torque τ = MB sinθ aligns needle with Earth's B field (~ $5 \times 10^{-5}$ T); equilibrium at θ = 0°; dip angle measures vertical component of Earth's field
Electromagnets: Soft iron (low coercivity) inside solenoid; B = μᵣμ_{0}nI amplified by factor μᵣ up to 10^{5}; switch on/off by controlling current; used in cranes, MRI quench valves, relay switches