A particle moves along line segments from the origin to the points(3,0,0),(3,3,1),(0,3,1), and back to the origin under the influence of the force field F(x,y,z)=z^2i+3xyj+4y^2k. Use Stokes' Theorem to find the work done.

glasskerfu 2021-02-09 Answered
A particle moves along line segments from the origin to the points(3,0,0),(3,3,1),(0,3,1), and back to the origin under the influence of the force field F(x,y,z)=z2i+3xyj+4y2k.
Use Stokes' Theorem to find the work done.
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Expert Answer

Malena
Answered 2021-02-10 Author has 83 answers

Step 1
From stokes theorem F.dr=×FdS.
Thus, calculate the curl of F=z2i+3xyj+4y2k:
×F=[ijkxyzz23xy4y2]
=8yi+2zj+3yk
Step 2
Thus, F.dr=(8ydydz+2zdxdz+3ydxdy). Now as per the given information 0x3,0y3and0z1.
Therefore the integral becomes:
F.dr=z=01y=038ydydz+z=01x=032zdxdz+x=03y=033ydxdy
=12(8×32+2×3+3×3×32)
=1592
=79.5 unit
Step 3
Thus work done is 79.5 unit.

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