# Encyclopedia Magnetica

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calculator:solenoid_thick

#### Calculator of H along axis of round "thick" solenoid

Magnetic field strength H of a circular “thick” solenoid along its axis
$$H(t,x) = \frac{I(t) · N}{L·(D-d)}· \left( \left( \frac{L}{2}+x \right) ·\ln \frac{D+\sqrt{D^2+(L+2·x)^2}}{d+\sqrt{d^2+(L+2·x)^2}} + \left( \frac{L}{2}-x \right)·\ln \frac{D+\sqrt{D^2+(L-2·x)^2}}{d+\sqrt{d^2+(L-2·x)^2}} \right)$$ (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.