[SPLIT] approximate the change in magnitude of...

[StintedVisions]

I'm having to accomplish a similar problem to the one discussed here, and the professor only covered half of this section.

approximate the change in magnitude of the electrostatic force between two charges when the distance between them increase from r=21m to r =22m
F(r)= 0.02/(r^2).

@tkhunny: I'm trying to figure out how you came to this... [FONT=MathJax_Math]d[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.01[/FONT][FONT=MathJax_Main]⋅[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Math]r[/FONT], I'm assuming that for mine it would be slightly different but using the quotient rule for derivatives I come up with a different solution.

@Subhotosh Khan: I tried using.. [FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]22[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.01[/FONT][FONT=MathJax_Main]484[/FONT]

[FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]21[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.01[/FONT][FONT=MathJax_Main]441[/FONT]

[FONT=MathJax_Math]δ[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]|[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]22[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]21[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]|....[/FONT] I come up with -4.03x10^-6, however they're telling me the solution is -4.32x10^-6.

I'm at a loss.

 

[tkhunny]

\(\displaystyle F(r) = 0.02r^{-2}\)

\(\displaystyle dF = 0.02(-2)r^{-3}dr\)

\(\displaystyle r = 21 m\)

\(\displaystyle dr = 22 m - 21 m = 1 m\)

\(\displaystyle dF = 0.02(-2)(21 m)^{-3}(1 m) = -4.319188e-6 / m^{2}\)

What are you missing?

 

[Deleted member 4993]

I'm having to accomplish a similar problem to the one discussed here, and the professor only covered half of this section.

approximate the change in magnitude of the electrostatic force between two charges when the distance between them increase from r=21m to r =22m
F(r)= 0.02/(r^2).

@tkhunny: I'm trying to figure out how you came to this... [FONT=MathJax_Math]d[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.01[/FONT][FONT=MathJax_Main]⋅[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Math]r[/FONT], I'm assuming that for mine it would be slightly different but using the quotient rule for derivatives I come up with a different solution.

@Subhotosh Khan: I tried using.. [FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]22[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.01[/FONT][FONT=MathJax_Main]484[/FONT]

[FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]21[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.01[/FONT][FONT=MathJax_Main]441[/FONT]

[FONT=MathJax_Math]δ[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]|[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]22[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]21[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]|....[/FONT] I come up with -4.03x10^-6, however they're telling me the solution is -4.32x10^-6.

I'm at a loss.

F = 0.2 * r^-2

dF = 0.2*(-2)*r^-3 dr = (-0.4)*r^-3 dr (you can use quotient rule - but that complicates things unnecessarily.)

dF = (-0.4)*r^-3 dr = (-0.4)*(21)^-3 (1) = -4.31919E-06 → your book must have used this method.

However,

[FONT=MathJax_Math]δ[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]|[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]22[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]21[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]|=[/FONT]4.03x10-6 this is more accurate answer

 

[DrPhil]

F = 0.2 * r^-2

dF = 0.2*(-2)*r^-3 dr = (-0.4)*r^-3 dr (you can use quotient rule - but that complicates things unnecessarily.)

dF = (-0.4)*r^-3 dr = (-0.4)*(21)^-3 (1) = -4.31919E-06 → your book must have used this method.

However,

[FONT=MathJax_Math]δ[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]|[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]22[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]21[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]|=[/FONT]4.03x10-6 this is more accurate answer

Key word in the question was "Approximate." They want you to use linear extrapolation (first derivative) to see how good (or poor) an approximation it is.