# Talk:QB/d cp2.11

cross product

${\displaystyle |{\vec {a}}\times {\vec {b}}|}$${\displaystyle =ab\sin \theta \Leftrightarrow }$ ${\displaystyle ({\vec {a}}\times {\vec {b}})_{x}=(a_{y}b_{z}-a_{z}b_{y})}$, ${\displaystyle ({\vec {a}}\times {\vec {b}})_{y}=(a_{z}b_{x}-a_{x}b_{z})}$, ${\displaystyle ({\vec {a}}\times {\vec {b}})_{z}=(a_{x}b_{y}-a_{y}b_{x})}$
Magnetic force: ${\displaystyle {\vec {F}}=q{\vec {v}}\times {\vec {B}},\;}$${\displaystyle d{\vec {F}}=I{\overrightarrow {d\ell }}\times {\vec {B}}}$.
${\displaystyle {\vec {v}}_{d}={\vec {E}}\times {\vec {B}}/B^{2}}$=EXB drift velocity
Circular motion (uniform B field): ${\displaystyle r={\tfrac {mv}{qB}}.\;}$ Period=${\displaystyle T={\tfrac {2\pi m}{qB}}.\;}$

Hall effect

Dipole moment=${\displaystyle {\vec {\mu }}=NIA{\hat {n}}}$. Torque=${\displaystyle {\vec {\tau }}={\vec {\mu }}\times {\vec {B}}}$. Stored energy=${\displaystyle U={\vec {\mu }}\cdot {\vec {B}}}$.
Hall field =${\displaystyle E=V/\ell =Bv_{d}={\tfrac {IB}{neA}}}$
Lorentz force =${\displaystyle q\left({\vec {E}}+{\vec {v}}\times {\vec {B}}\right)}$