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. * 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 .

Work done . 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