A force field in the -plane is given by

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

A force field in the

xy

-plane is given by

\mathbf F = 6x\,\hat\imath + 4y\,\hat\jmath\;\text{N}

. Which one of the following potential energy functions

U(x,y)

(in joule) correctly corresponds to this force? (Assume the usual relation

\mathbf F = -\nabla U

.) (a)

U = 3x^{2} + 2y^{2} + C

(b)

U = -3x^{2} - 4y^{2} + C

(c)

U = -3x^{2} - 2y^{2} + C

(d)

U = -2x^{2} - 3y^{2} + C