Coil / Conductor Field
Solenoid B=μ₀nI · long wire B=μ₀I/2πr · loop centre B=μ₀I/2R.
Magnetic Pressure → Coil Hoop Stress
P=B²/2μ₀; hoop σ=P·r/t; min former thickness for σ_allow.
Larmor Radius & Cyclotron Frequency
r_L=mv⊥/qB; f_c=qB/2πm.
Stored Energy & Density
E=½LI²; energy density u=B²/2μ₀.
Force on Current Conductor
F = I·L×B (perpendicular).
Electrostatic Pressure
P = ½ε₀E²; on electrodes at field E.
Formula reference
B: solenoid μ₀nI, wire μ₀I/2πr, loop μ₀I/2R. P_mag=B²/2μ₀, hoop σ=Pr/t.
r_L=mv⊥/qB, f_c=qB/2πm; E=½LI², u=B²/2μ₀; F=BIL; P_E=½ε₀E².