15.3 Independence of the Path by SGLee, HSKim, 오교혁
1-6. Determine whether or not the vector field is conservative. If it is conservative, find a potential of 
.
1. 
Not conservative, since curl
.
SKKU-Calculus-Sec-15-3 Independence of the Path, SGLee+오교혁
15.3 Independence of the Path by SGLee, HSKim, 오교혁
1-6. Determine whether or not the vector field is conservative. If it is conservative, find a potential of .
1.
Not conservative, since curl.
2. 
Not conservative.
3. 
Not conservative.
4. 
Since, curl 
, 
is conservative.
―(1)
Taking partial derivative of 
with respect to 
, we get 
. Hence from (1) we get
―(2)，thus 
―(3)
Now taking partial derivative of 
with respect to 
we get 
. Hence from (3) we get
, a constant. Therefore, 
.
5. 
Not conservative.
6. 
Conservative, 
.
7. Show that the vector field 
is not conservative.
Since curl
, 
is not conservative.
8. Determine whether the force field 
is a conservative field.
http://matrix.skku.ac.kr/cal-lab/cal-14-2-5.html
* 위의 명령어로 표현돤 결과는 vector 로 표현되서 보기 편하다.
Ans: 
, hence 
is not conservative field.
|
9. a. Prove that 
is a conservative field.
b. Find its scalar potential 
.
c. Also find the work done in moving an object in this field from 
to 
.
http://matrix.skku.ac.kr/cal-lab/cal-15-2-6.html
Scalar potential 
.
Work done
.
10. Find the total work done in moving a particle by a force field 
along the curve 
form 
to 
.
http://matrix.skku.ac.kr/cal-lab/cal-15-2-8.html
