SaM - Geometrical Magneto Resistance

Remeber:

Starting from the current density equation:$\vec{J}=nq\vec{v}=\sigma \vec{E}$We can rewrite it as:$\vec{v}=\mu \vec{E}$And if subject the carriers also to a magnetic field, the formula changes into:IMPORTANTE $\vec{v}=\mu \vec{E}+\mu (\vec{v}\times \vec{B})$This is the “geometrical magneto resistance formula”. Where:

• $\vec{v}$ is the velocity of carriers.
• $\mu$ is the mobilty of carriers.
• $E$ is the electric field.
• $\vec{B}$ is the magnetic field density

We can solve for $\vec{v}$ and find a formula depending only on $\mu ,\vec{B},\vec{E}$: (NOT IMPORTANT)$\vec{v}=\frac{\mu }{1+{\mu }^2{B}^2}\left(\vec{E}+\mu \left(\vec{E}\times \vec{B}\right)+{\mu }^2\left(\vec{B}\vec{E}\right)\vec{B}\right)$

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Memory Card

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• There is an error, it should be:$\frac{\mu }{1+{\mu }^2{B}^2}(\dots )$