Parameters
Presets
Coil Type
Wire Diameter d
0.50 mm
Coil Diameter D
20.0 mm
Coil Length l
50.0 mm
Turns N
100
Current I
1.00 A
Core Material
—
Inductance L
—
Center Field B₀
—
End Field B_end
—
Coil Resistance R
—
Stored Energy U
—
Time Constant τ = L/R
Theory
Single-layer solenoid inductance (long solenoid approximation):
$$L \approx \frac{\mu_0 \mu_r N^2 A}{l}, \quad A = \pi\left(\frac{D}{2}\right)^2$$Center magnetic field: $B_0 = \dfrac{\mu_0 \mu_r N I}{l}$ (infinite length approximation)
Finite solenoid axial field (Biot-Savart): $B(z) = \dfrac{\mu_0 \mu_r N I}{2l}\left(\cos\theta_1 - \cos\theta_2\right)$
Coil resistance: $R = \dfrac{\rho \cdot N \pi D}{\pi (d/2)^2}$, Stored energy: $U = \dfrac{1}{2}LI^2$
CAE Note: Inductance estimation for electromagnetic actuators and relay design / inductor selection for switching power supplies / EMC filter design / preliminary MRI and NMR magnet design. Can be combined with field analysis software (ANSYS Maxwell / JMAG) for detailed simulation.