Solenoid Magnetic Field Optimizer

Thresholds

Max B (T): Max Layers: Max Thick (mm): Max Wire (m): Max Power (W): Max Resistance (Ω):

Input Parameters

Solenoid Length (cm):50 cm

Solenoid Offset (on each side) (mm):5 mm

Solenoid Outer Radius (cm):10 cm

Solenoid Inner Radius (cm):5 cm

Diameter of Wire (cm):*0.259 cm bare, 0.025 cm insulation

Current (A):2 A

Resistivity (×10⁻⁶ Ω·cm):1.68 ×10⁻⁶ Ω·cm

Linear Mass Density (g/cm³):8.92 g/cm³

Input Parameters

Solenoid Length (cm):50 cm

Solenoid Offset (on each side) (mm):5 mm

Solenoid Outer Radius (cm):10 cm

Solenoid Inner Radius (cm):5 cm

Diameter of Wire (cm):*0.259 cm bare, 0.025 cm insulation

Magnetic Field (T):0.01 T

Resistivity (×10⁻⁶ Ω·cm):1.68 ×10⁻⁶ Ω·cm

Linear Mass Density (g/cm³):8.92 g/cm³

Results

Logging

Wire	Electrical	Magnetic	Mechanical	Action

Animation

Equations Used

ntp = (L_solenoid - (2 * L_soloff)) / D_wire

n_layers = (2 / sqrt(3)) * ((R_max - R_min) / D_wire - 1) + 1

n_T = ntp * n_layers

lw = 2 * π * ntp * n_layers * (R_min + 0.5 * D_wire + (√3 / 4) * D_wire * (n_layers - 1))

A_cross = π * (D_bare / 2)²

V = A_cross * lw

mw = ρ * V

t_total = D_wire * (1 + (√3 / 2) * (n_layers - 1)) * 10

n = n_T / L_solenoid

Current I Mode: B = μ₀ * n * I

Magnetic Field B Mode: I = B / (μ₀ * n)

R = ρ * lw / A_cross

P = I² * R

Assumptions: Hexagonal packing of wires. The wire length formula uses an average radius approximation, assuming constant turns per layer (ntp). Density (ρ) is user-selected (g/cm³). Resistivity (ρ) is user-selected (×10⁻⁶ Ω·cm, converted to Ω·m). μ₀ = 4π × 10⁻⁷ H/m. All lengths are in meters, density in g/cm³, thickness in mm, magnetic field in tesla, resistance in ohms, and power in watts.

* Wire diameters based on annealed copper at 20 °C from "Copper wire tables," United States National Bureau of Standards, 1914, https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook100.pdf