PX155 - C5 - power

dg-publish: true

work performed per unit time
measured in $J s^{- 1}$ or $w a t t s (W)$
since $d W = \vec{F} . d \vec{r}$

\frac{d W}{d t} = \vec{F} \cdot \frac{d \vec{r}}{d t} = \vec{F} \cdot \vec{v}

eg: the "lorentz force" is a force that acts on a particle of charge $q$ as it moves through an electric field $\vec{E}$ and a magnetic field $\vec{B}$

\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})

- what is the rate of work done by $\vec{F}$
$P = \frac{d W}{d t} = \vec{F} \cdot \vec{v}$
$P = q \vec{E} \cdot \vec{v} + q (\vec{v} \times \vec{B}) \cdot \vec{v}$
$P = q \vec{E} \cdot \vec{v} ⟹ \vec{B} - f i e l d$ does no work