point, loop radius) k = lambda r, x, a : sqrt ( 4 * al ( r, a ) / Q ( r, x, a )) # k = f(radius, distance to meas. point) Q = lambda r, x, a : ( 1 + al ( r, a )) ** 2 + be ( x, a ) ** 2 # Q = f(radius, distance to meas. point, radius of loop) ga = lambda x, r : x / r # Gamma = f(axial distance, radius to meas. constant) al = lambda r, a : r / a # Alpha = f(radius of measurement point, radius of loop) be = lambda x, a : x / a # Beta = f(axial distance to meas. a # Central field = f(current, loop radius, perm. $E(k)$ is the complete elliptic integral function, of the second kind.įrom scipy.special import ellipk, ellipe, ellipkm1 from numpy import pi, sqrt, linspace from pylab import plot, xlabel, ylabel, suptitle, legend, show uo = 4E-7 * pi # Permeability constant - units of H/m Bo = lambda i, a, u = uo : i * u / 2. $K(k)$ is the complete elliptic integral function, of the first kind $r$ is the distance in the radial direction from the axis of the current loop to the field measurement point. $x$ is the distance in the axial direction from the center of the current loop to the field measurement point. $\mu_0$ is the permeability constant (approx. $i$ is the current in the loop wire (Amperes)
