Need to check work Thanks for your time Consider a ferromagn

Need to check work. Thanks for your time.

Consider a ferromagnetic material having an initial relative permeability of 5000 is to be used for the fabrication of a toroidal inductor. The toroidal core is round, blit has a square cross section as shown in the figure below. Outer diameter of the core is 0.375 inch and the inner diameter is 0.187 inch. Calculate the number of turns required to achieve an inductance of 10 mH. If the current through the inductor is 10A. calculate the magnetic field strength, the magnetic flux density at the center of the core, and the total amount of energy stored in the magnetic field, Calculate length of the toroid using the mean radius. Left: the circular toroidal core: Right: square shaped cross-section of the toroid.

Solution

a) http://www.66pacific.com/calculators/toroid_calc.aspx

n = 231 (r_m=0.281 inch)

b) H =0.628318530 * 10^-4 T (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html)

H (center, at z =0.07m)= 0.623 * 10^-4 T (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html)

energy stored u = (5000) H.H/2 = 900 Joules.