- #1

a4b3c2d1e0f

- 3

- 0

We start with [itex]P = {\bf F} \cdot {\bf v}[/itex], where [itex]{\bf v} = \frac{d\bf r}{dt}

[/itex]

We know that the force exerted on a test charge

*q*is given by [itex]{\bf F} = {\bf E} q[/itex], and for voltage we know [itex]dV = - {\bf E} \cdot dx[/itex].

Inserting

*in equation for power, we get [itex]P = {\bf E}q \cdot \frac{d\bf x}{dt} = {\bf E}\cdot dx \frac{q}{dt} = - dV \frac{q}{dt} .[/itex]*

**F**How would I go from this, to the desired result, without taking a "quantum leap"?

Is there a better way to actually derive this mathematically impeccably?