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lorenz0

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- Homework Statement
- A solenoid ##L = 10 cm ## long with radius ##r << L## consisting of ##N=100## coils with a current ##i## through it is completely filled with a cylinder of ferromagnetic material whith a curve of first magnetization as shown in the figure. Estimate the value of the magnetization field ##M## assuming that the magnetic working point is at ##H = 4 kA / m##.

In this condition, calculate the current ##i## flowing through the solenoid and the total magnetization current present on the lateral surface of the ferromagnetic cylinder.

- Relevant Equations
- ##\vec{H}=\mu_0 \frac{N}{L} i##, ##\sigma_{m}=\vec{M}\cdot \hat{n}##

From the graph we see that at ##H=4 kA/m,\ B=1.5T##.

We have that ##M=\frac{B}{\mu_0}-H=\frac{1.5T}{\mu_0}-4kA/m## and from Ampere's Law that ##i=\frac{HL}{N}=\frac{4kA/m\cdot 0.1 m}{100}## and the current (density on the surface is) ##\sigma_{m}=M##.

Does this make sense? I am having difficulties in understanding the concept of magnetic working point and how ##\vec{B},\ \vec{H},\ \vec{M}## work together when magnetic fields interact with matter so I would be grateful for some feedback.

We have that ##M=\frac{B}{\mu_0}-H=\frac{1.5T}{\mu_0}-4kA/m## and from Ampere's Law that ##i=\frac{HL}{N}=\frac{4kA/m\cdot 0.1 m}{100}## and the current (density on the surface is) ##\sigma_{m}=M##.

Does this make sense? I am having difficulties in understanding the concept of magnetic working point and how ##\vec{B},\ \vec{H},\ \vec{M}## work together when magnetic fields interact with matter so I would be grateful for some feedback.