Question

The potential energy of a particle in a space is given by $U=x^2+y^2$. Find the force associated with this potential energy:

• A. $-2x\hat{i}-2y\hat{j}$
• B. $2x\hat{i}-2y\hat{j}$
• C. $-2x\hat{i}+2y\hat{j}$
• D. $2x\hat{i}+2y\hat{j}$

Answer 1

The correct option is A $-2x\hat{i}-2y\hat{j}$

$F_x=\frac{-\partial u}{\partial x}=-[2x+0]=-2x$

$F_y=\frac{-\partial u}{\partial y}=-(2y+0)=-2y$

$\overrightarrow{F}=-2x\hat{i}-2y\hat{j}$