help with an exam study guide question! i've never missed a class and never seen this question or went into more detail about it. I didn't see this on any homework assignments but could someone give me the rundown on this question?

Question

zephyr141 · Answer

The Coulomb Force is the force between two electrical charges. The potential energy associated with this force is$$U_{coulomb}(0)=\frac{1}{4\pi \epsilon_{0}}\frac{q_{1}q_{2}}{x}$$and epsilon(0), q(1) and q(2) are constants. Find the Coulomb force.
a)$$F_{coulomb}(x)=\frac{1}{4\pi \epsilon_{0}}q_{1}q_{2}\ln x $$b)$$F_{coulomb}(x)=\frac{1}{4\pi \epsilon_{0}}\frac{q_{1}q_{2}}{x^2}$$c)$$F_{coulomb}(x)=\frac{-1}{4\pi \epsilon_{0}}\frac{q_{1}q_{2}}{x^2}$$d)$$F_{coulomb}(x)=\frac{-2}{4\pi \epsilon_{0}}\frac{q_{1}q_{2}}{x^3}$$

anonymous · Answer

Energy is measured in units of Joules. A [ J ] is a [N m].

Force is measured in units of Newtons. So a force is just energy divided by a displacement in meters.

If the potential energy function has 1/x dependence, then the force would have (1/x) / (x) = 1/(x^2) dependence.