A conservative force field is defined as one for which the
net work done on an object in a closed path is zero. That is,
the force field 
is conservative if
for any closed path c contained in the field of .
Such a field of force can always be represented as the gradient of a scalar function defined by
where the path of integration is arbitrary. The scalar function
is referred to as the potential of the conservative
force in question. If the function is known
then the force can be determined from the relation
Thus the force is normal to the equiscalar surfaces of .
The physical interpretation of can be seen from
Eq. (61) to be the work done against the force field in moving
from the reference position (0,0,0) to the
position (x,y,z). An object situated at (x,y,z) therefore
has an intrinsic or potential energy which differs from that
which it would have at position (0,0,0) by the
amount .