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Calculator of H along axis of round "thick" solenoid

Magnetic field strength H of a circular “thick” solenoid along its axis
H(t,x)=I(t)·NL·(Dd)·((L2+x)·lnD+D2+(L+2·x)2d+d2+(L+2·x)2+(L2x)·lnD+D2+(L2·x)2d+d2+(L2·x)2) (A/m)
where: I(t) - current (A) at time t (s), N - total number of turns (unitless), L - length of the solenoid (m), d - inner diameter of the solenoid (m), D - outer diameter of the solenoid (m), x - location (m) from the centre of the solenoid (the centre is located at the point x = 0)
“Thick” solenoid (d<D) with a circular cross-section

Current I =     

Inner diameter d =     

Outer diameter D =

Length L =     

Number of turns N = (unitless)

Position on axis x =



H =        B0) =

Notes: This equation is valid only for uniformly wound solenoid, with uniform current distribution in each turn. The instantaneous values of H are directly proportional to the instantaneous values of I. The value of B(μ0) is for vacuum.