approximate the change in the magnitude

Question

approximate the change in the magnitude of the electrostatic force between two charges when the distance between them i increases from r=25 m to r=26 m (F(r)=0.02/r^2)

 

Between r=25m and r=26m, the magnitude of the electrostatic force between two charges changes by___________.(Use scientific notation. Round to two decimal places as needed.)

Answer 1

You can approximate the change in a function by finding the slope of the function at a given point and extrapolating where the function would be if the slope did not change.

 

F(r) = 0.02 r^-2

F'(r) = 0.02 (-2 r^-3)

F'(r) = -0.04 r^-3

F'(25) = -0.04 (25)^-3

F'(25) = -2.56 × 10^-6

F'(25) * Δr = (-2.56 × 10^-6) * (26-25)

approximate change = -2.56 × 10^-6