▁as ▁the ▁negative ▁of ▁this ▁scalar ▁field ▁so ▁that ▁work ▁by ▁the ▁force ▁field ▁decre ases ▁potential ▁energy , ▁that ▁is ▁ ▁In ▁this ▁case , ▁the ▁application ▁of ▁the ▁del ▁operator ▁to ▁the ▁work ▁function ▁yields , ▁ ▁and ▁the ▁force ▁F ▁is ▁said ▁to ▁be ▁" der iv able ▁from ▁a ▁potential ." ▁This ▁also ▁necessarily ▁implies ▁that ▁F ▁must ▁be ▁a ▁conserv ative ▁vector ▁field . ▁ ▁The ▁potential ▁U ▁defines ▁a ▁force ▁F ▁at ▁every ▁point ▁x ▁in ▁space , ▁so ▁the ▁set ▁of ▁forces ▁is ▁called ▁a ▁force ▁field . ▁ ▁Comput ing ▁potential ▁energy ▁Given ▁a ▁force ▁field ▁F ( x ), ▁evaluation ▁of ▁the ▁work ▁integral ▁using ▁the ▁gradient ▁theorem ▁can ▁be ▁used ▁to ▁find ▁the ▁scalar ▁function ▁associated ▁with ▁potential ▁energy . ▁ ▁This ▁is ▁done ▁by ▁introdu cing ▁a ▁parameter ized ▁curve ▁ γ ( t )= r ( t ) ▁from ▁ γ ( a )= A ▁to ▁ γ ( b )= B , ▁and ▁computing , ▁ ▁For ▁the ▁force ▁field ▁F , ▁let ▁v = ▁dr / dt , ▁then ▁the ▁gradient ▁theorem ▁yields , ▁ ▁The ▁power ▁applied ▁to ▁a ▁body ▁by ▁a ▁force ▁field ▁is ▁obtained ▁from ▁the ▁gradient ▁of ▁the ▁work , ▁or ▁potential , ▁in ▁the ▁direction ▁of ▁the ▁velocity ▁v ▁of ▁the ▁point ▁of ▁application , ▁that ▁is ▁ ▁Ex amples ▁of ▁work ▁that ▁can ▁be ▁computed ▁from ▁potential ▁functions ▁are ▁gravity ▁and ▁spring ▁forces . ▁ ▁Pot ential ▁energy ▁for ▁near ▁Earth ▁gravity ▁