Question

A particular potential energy field can be described by the function $U\left(x\right)=\frac{1}{x^2}$ for all real values of $x$, where $U\left(x\right)$ and $x$ are in standard units.
What is the force magnitude exerted on a particle at the position $x=3$?

• A. $\frac{1}{3}$
• B. $\frac{2}{27}$
• C. $\frac{1}{9}$
• D. $\frac{2}{9}$
• E. $\frac{2}{3}$

Answer 1

Answer: (B)

$\frac{2}{27}$

The potential energy $U\left(x\right)=\frac{1}{x^2}$

Thus force acting on the particle $F=\frac{dU\left(x\right)}{dx}=\frac{-2}{x^3}$

$\therefore$ Magnitude of force at $x=3$ m $|F|{|}_{x=3}=\frac{2}{3^3}=\frac{2}{27}$ N