OpenStax University Physics/E&M/Magnetic Forces and Fields

For quiz at QB/d_cp2.11
$$|\vec a\times\vec b|$$$$=ab\sin\theta \Leftrightarrow$$ $$(\vec{a} \times \vec{b})_x = (a_yb_z - a_zb_y)$$, $$(\vec{a} \times \vec{b})_y = (a_zb_x - a_xb_z)$$, $$(\vec{a} \times \vec{b})_z = (a_xb_y - a_yb_x)$$ Magnetic force: $$\vec F=q\vec v\times\vec B,\;$$$$d\vec F = I\overrightarrow{d\ell}\times\vec B$$. $$\vec v_d=\vec E\times\vec B/B^2$$=EXB drift velocity Circular motion (uniform B field): $$r=\tfrac{mv}{qB}.\;$$ Period=$$T=\tfrac{2\pi m}{qB}.\;$$ Dipole moment=$$\vec\mu=NIA\hat n$$. Torque=$$\vec\tau=\vec\mu\times\vec B$$. Stored energy=$$U=\vec\mu\cdot\vec B$$. Hall field =$$E=V/\ell=Bv_d=\tfrac{IB}{neA}$$ Lorentz force =$$q\left(\vec E + \vec v\times\vec B\right)$$