# Potential Energy is defined only in conservative fields?

I am currently preparing for my physics test and struck in this question

Q. Potential Energy is defined:

1}only in conservative fields

2}As negative of work done by conservative forces

3}As negative of work done by external forces, when change in Kinetic energy is zero

As I read my study material it read :The work done by conservative forces is equal to decrease in Potential energy of system giving (2) as true and when its true then (3) also must be true by Conservation of mechanical Energy (I had done many question on it so related that with it )

But correct answer was (1) only

Can you help me out

• (2) and (3) give change in PE. – Rick Dec 7 '17 at 10:18
• @Rick MEANS THEY ARE CORRECT? – TreaV Dec 7 '17 at 10:23
• Means they are incorrect. "x" and "the change in x" are two different things. – Chris Dec 7 '17 at 10:28
• Sorry didn't got it clearly , but are you saying its true for change in potential energy not for potential Energy?@Chris – TreaV Dec 7 '17 at 10:38
• If the change in KE is zero then the external force is opposite (and equal) to the force exerted by the field. So the work done by external force is positive. So even if you think about change in PE, 3 is not correct. – nasu Oct 22 '18 at 14:40

A conservative force, $$\vec{F}= - \nabla \vec{V}$$. This implies that, for the conservative filed, force could be derived from the potential. For a non conservative field, the force could not be derived from the potential, as such potential exist in differential form and it would be impossible to write the potential explicitly as a function and hence the potential energy can only be defined for the conservative fields.