Chapter One: Vector Analysis The use of vectors and vector analysis ...

Electromagnetic Theorem
(Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department
Integral Calculus:
1‐ Line integrals (Path):
A line integral is an expression of
the form,
∙
where is a vector function,
is the infinitesimal displacement vector.
And the integral is to
be carried out along a prescribed path from point to point .
If the path in question forms a closed loop (that is if ), I shall put a circle on the integral
sign:
∙
Example of line integrals is the work done by
a force :
∙
Ordinarily, the value of a line integral depends critically on the particular path taken from
to .
But if the
line integral is independent of the path; a force
that has this property is called
Conservative.
Example:
Calculate
the line integral of the function 2 1 from the point
1 ,1
, 0 to the point 2 , 2 , 0 along the paths 1 & 2 in Fig. What is
∮ ∙
for the loop
that goes from to along 1 and returns to along 2?