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 .
Not conservative, since curl.
Since, curl , is conservative.
Taking partial derivative of with respect to , we get . Hence from (1) we get
Now taking partial derivative of with respect to we get . Hence from (3) we get
, a constant. Therefore, .
7. Show that the vector field is not conservative.
Since curl, is not conservative.
8. Determine whether the force field is a conservative field.
* 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 .
Scalar potential .
10. Find the total work done in moving a particle by a force field
along the curve form to .
Plenary Speaker at AMC 2013, Bexco, Korea