The potential of, A, of a charge distribution at a point on the positive x-axis is given for x in centimeters, by
A= 2pi [sqrt(x^2+4)-x]
A particle at x=3 is moving to the left at a rate of 0.2 cm/sec. At what rate is it potential changing?

Question

The potential of, A, of a charge distribution at a point on the positive x-axis is given for x in centimeters, by 
A= 2pi [sqrt(x^2+4)-x]
A particle at x=3 is moving to the left at a rate of 0.2 cm/sec.  At what rate is it potential changing?

anonymous · Answer

any help would be appreciated! Thank you!!!

anonymous · Answer

Differentiate with respect to $t$:
$$\frac{dA}{dt}=2\pi\frac{d}{dt}\left[\sqrt{x^2+4}-x\right]$$
Once you do that, you plug in $x=3$ and $\dfrac{dx}{dt}=-0.2$ (negative because we assume the direction to the right of the origin is positive). Find $\dfrac{dA}{dt}$.