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.



      Not conservative.



      Not conservative.




        Since, curl  is conservative.


      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, .



      Not conservative.



      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


                                             Back to Part II