Question

Suppose P(x,y) i + Q(x,y) j is a two dimensional vector field. Show that F is irrotational if dP/dY = dQ/dX

Answer 1

basically you want to show curl = 0

Answer 2

alright, but can you help me solve it?

Answer 3

\(Curl(F) = \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 0 \)

Answer 4

can you show me the steps to where you got that?

Answer 5

thats the definition of Curl
\(Curl(F) = \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \)

Answer 6

Since you're given that both partials are equal, the Curl equals 0.

since Curl = 0, there wont be any rotation component

Answer 7

alright

Answer 8

clearly that doesnt look very exciting,
I think you're looking for proving it without using definition of Curl ?

Answer 9

@eliassaab @sourwing

Answer 10

not sure really but its a 2 mark question, so i think its correct

Answer 11

ahh ok :) then just show that Curl of vector field equals 0, so the force cannot cause any rotation effects

Answer 12

alright bro thanks for your help, it turned out easier than i expected

Answer 13

its almost suspicious

Answer 14

hhaha okay, np :)

Answer 15

:)