ps.pdf - MATH 317 PROBLEM SET III SOLUTIONS 1 Determine whether or not each of the following vector fields are conservative Find the potential if it is

ps.pdf - MATH 317 PROBLEM SET III SOLUTIONS 1 Determine...

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MATH 317 PROBLEM SET III SOLUTIONS 1)Determine whether or not each of the following vector fields are conservative. Find the potential if it is.a)~F(x, y, z) =xˆı-2yˆ|+ 3zˆkb)~F(x, y) =xˆı-yˆ|x2+y2c)~F(x, y) =yˆı-xˆ|x2+y22-y2+32)is conservative. Solution. c)~F(x, y) =r(tan-1xy2)Let~Fbe a conservative force field with potentialφ. Show that the lines of force are perpendicular to theequipotential surfaces. 3)Find the velocity field for a two dimensional incompressible fluid when there is a point source of strengthmat the origin. That is, fluid is emitted from the origin at area rate 2mcm2/sec. Show that this velocityfield is conservative and find its potential.

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