Qualitative study on how an applied current can be used to generate a permanent magnetization

💼 Case: consider a ferromagnetic substance with a current carrying wire wound around the substance. The wire carrying a current $I$.

• Since $\vec H=\vec H(I)$ modifying the current will modify the magnetic intensity vector which will modify the magnetic field

• When there is zero current applied $I=0$ the domains inside the ferromagnet are randomly aligned so that there is no net magnetization $|\vec M|\approx 0.$

• As the current is increased the domains begin to flip due to the energy input from the current carrying wire. The flip of domain causes $\vec H$ to increase causing an increase in the magnetic field $\vec B=\mu_r\mu_0 \vec H$ and magnetization $\vec M\propto \vec B$

  💃 Example: typically $\mu_r\approx 1000$

• If the current continues to increase the magnetization will reach a maximum $\vec M=\vec M_\text{max}$ when all domains in the substance are aligned the only way of increasing the magnetic field is by a slow linear increase in $\vec H$

• If we reduce the current along the curve $A\to B$ some domains will flip back but not all which leaves a remnant magnetization so that $\vec M$ will remain significant.

  At $B$ there is zero applied current $\vec H=0$ and the magnetization is permanent.

• If we now apply an opposite current we travel along $B\to C$ at which point enough of the domain will have flipped to cancel out the magnetic field. This value of $\vec H=\vec H_C$ is called the coercive field

• Between $C\to D$ the domains all begin to flip in the opposite direction until magnetization saturation occurs at $D$

• 🔋 The work done along the round trip

  $$ A\to B\to C\to D\to E\to F\to A $$

  is given by

  $$ U=-V\oint\vec H \cdot \text d\vec B $$

  which is the area under the hysteresis curve

  

  Hysteresis curve