The following potential is given:
u = –x 2 y – 2z + 9
(i) Find the three-dimensional force field from that potential. Is the force conservative?
(ii) Calculate the work done by the force in moving a particle from the origin to (1, 2, 4),
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. (i) The force field is
= – 
u = – 
= 2xy 
+ x 2 
+ 2 
…..(i)
The force is conservative, because the force is derived from a potential function 
= – 
u.
(ii) Because the force is conservative, the work is independent of the path. Therefore, we can choose a path from (0, 0, 0) to (1, 2, 4) and integrate 
. For instance, If we parametrize the path with a parameter t , so that:
…...(iii)
We obtain (dz = 4 dt, dy = 2 dt, dx = dt):
W = 
…. (iv)
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems