Module 16 : Line Integrals, Conservative fields Green's Theorem and applications
Lecture 47 : Fundamental Theorems of Calculus for Line integrals [Section 47.1]
We
have
47.1.2
Applications :
(i)
Independence of work done:
The above theorem says that if a vector-field is conservative, then the work done in moving from one point to another does not depend upon the path taken.
(ii)
Principle of energy conservation:
Let be a conservative force field in a domain with
The scalar field is called a potential function for the vector field and the scalar field
is called the potential energy of the field at the point . The above theorem tells us that the work done by on a particle that moves along any path from a point to a point is related to the potential energy of the body by the equation
be a conservative force field in a domain 
with 
is called a potential function for the vector field 
and the scalar field 
. The above theorem tells us that 
the work done by 
on a particle that moves along any path 
from a point 
to a point 
is related to the potential energy of the body by the equation 
