- #1
JD_PM
- 1,131
- 158
Homework Statement
Homework Equations
$$F = \nabla \phi$$
$$| F | = \sqrt{F \cdot F}$$
The Attempt at a Solution
I want to compute ##| F | = \sqrt{F \cdot F}##
$$| F | = \sqrt{F \cdot F} = \sqrt{\frac{(km)^2 (r-r_0)^2}{|r-r_0|^6}} = \sqrt{\frac{(km)^2}{(r-r_0)}} = \frac{km}{(r-r_0)^{1/2}} = \frac{km}{|r-r_0|} $$
That seems to be OK. I have one doubt here; would the following equality hold?
$$(r-r_0)^2 = ((x-x_0) - (y-y_0) - (z-z_0))^2$$
I do not need it for getting | F | but I want to be sure of this.
Thanks.