Example problems of magnetic circuits

Given:

A copper core with susceptibility $\chi _{m}=-9.7x10^{-6}$

length of core L = 1 m

Gap length g = .01 m

cross sectional area A = .1 m

current I = 10A

N = 5 turns

Find: B

Solution: First we need to find the permeability of copper $\mu$ given by the equation
<math> \mu = \mu_0 (1 + \chi_m)

Which yeilds <math> \mu = 4*\pi*10^{-7}(1+-9.7x10^{-6}) = 1.2566x10^{-6}