Example problems of magnetic circuits

Given:

A copper core with susceptibility Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi_m = -9.7 &times 10^{-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
$\mu =\mu _{0}(1+\chi _{m})$

Which yeilds $\mu =4\times \pi \times 10^{-7}(1+-9.7\times 10^{-6})=1.2566\times 10^{-6}$

Now with this, the length and cross sectional area of the core we can solve for reluctance $R_{c}$ by:

<math> R_c = \frac{L}{\mu A} = \frac{1}{1.2566 \times 10^{-6}\times .1} = 7.96 \times 10^{6}