- #1

lorenz0

- 148

- 28

- Homework Statement
- Consider a ferromagnetic material and suppose we can approximate a portion of its hysteresis curve as a segment as shown in the figure. With this material we make a permanent magnet in the shape of a toroid with an overall length equal to ##D = 80 cm## including an air gap with a thickness of ##h = 5 mm##. Calculate the magnitude of the magnetization vector ##\vec{M}## of the magnet.

- Relevant Equations
- ##\vec{H}=\frac{\vec{B}}{\mu_0}-\vec{M}##

I have thought about the following

##\oint \vec{H}\cdot d\vec{l}=0\Leftrightarrow H_{int}(D-h)+H_{ext}h=0\Leftrightarrow (\frac{B}{\mu_0}-M)(D-h)+\frac{B}{\mu_0}h=0\Leftrightarrow M=\frac{D}{D-h}\frac{B}{\mu_0}## but (supposing what I have done is correct) I don't understand which value of ##B## I should take: perhaps the one at ##H=0\frac{kA}{m}##, namely ##B=0.5T##?

Thanks

##\oint \vec{H}\cdot d\vec{l}=0\Leftrightarrow H_{int}(D-h)+H_{ext}h=0\Leftrightarrow (\frac{B}{\mu_0}-M)(D-h)+\frac{B}{\mu_0}h=0\Leftrightarrow M=\frac{D}{D-h}\frac{B}{\mu_0}## but (supposing what I have done is correct) I don't understand which value of ##B## I should take: perhaps the one at ##H=0\frac{kA}{m}##, namely ##B=0.5T##?

Thanks