C3

"The force F newtons between two magnetic poles is given by the formula

$F = \displaystyle\frac{1}{500r^{2}}$ where r m is their distance apart.

Find the rate of change of the force when the poles are 0.2 m apart and the distance between them is increasing at a rate of 0.03 ms^-1"

$\displaystyle\frac{dF}{dt} = \frac{dr}{dt}*\frac{dF}{dr}$

dr/dt = 0.03 ms^-1 and df/dr = -1000r^-3.....where r = 0.2m so don't i just do for df/dr, -1000*(0.2^-3) and then multiply it by 0.03???

Thanks in advance.

Yes, but you've made a mistake in your differentiation for df/dr.

PS: "\times" will give you the multiply sign in LaTex

Thanks for your message but i don't see where i have gone wrong.....

1/500r^2 = 500r^-2 so df dr = -2*500r^-3 = -1000r^-3????

I could just tell you, but you make a lot of these little mistakes; so just telling you isn't helping.

So, go back over what I've quoted one character at a time if necessary.

oh yeah, 500 isn't a function.... just a constant, so that won't differentiate so we just have -2r^-3 = dF/dr???

Not quite.

However it is the constant term that is incorrect.

Oh don't tell me i forgot to add the - to the 500 when flipping the fraction over??? making it 1000 instead of -1000

Oh don't tell me i forgot to add the - to the 500 when flipping the fraction over??? making it 1000 instead of -1000

"The force F newtons between two magnetic poles is given by the formula

$F = \displaystyle\frac{1}{500r^{2}}$ where r m is their distance apart.

Find the rate of change of the force when the poles are 0.2 m apart and the distance between them is increasing at a rate of 0.03 ms^-1"

$\displaystyle\frac{dF}{dt} = \frac{dr}{dt}*\frac{dF}{dr}$

dr/dt = 0.03 ms^-1 and df/dr = -1000r^-3.....where r = 0.2m so don't i just do for df/dr, -1000*(0.2^-3) and then multiply it by 0.03???

Thanks in advance.

d/dr (r^-2) = -2r^-3

So it should be -2/500r^2 = -1/250r^3

I think.

I told you this because you don't seem to be getting anywhere with your constant :P:

Basically when calculating $\dfrac{dF}{dr}$ rewrite F as $F=\dfrac{r^{-2}}{500}$ and try differentiation again. In other words leave the constant alone whilst you're differentiating and simplify the resulting derivative.

sounds like a silly question but why do we leave the constant whilst differentiating?