Magnetic field strength H of a circular “thick” solenoid along its axis | |
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H(t,x)=I(t)·NL·(D−d)·((L2+x)·lnD+√D2+(L+2·x)2d+√d2+(L+2·x)2+(L2−x)·lnD+√D2+(L−2·x)2d+√d2+(L−2·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) |
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.