# Am i doing this right?

Here's the question:

Suppose we have a scalar field phi(r)=xy defined on the plane (x,y). Find th vector field gradient phi, and plot the result in a single graph atthe four points (1,1), (-1,1) (1,-1), (-1,-1) and at the four points (1,0),(0,1),(-1,0) and (0,-1).

Ans.

For the gradient of phi(r)=xy, I got yi + xj. Is this right?

one more questio

how will I plot it. Do i have to solve the eequation at each of those points and plot the answer that I get?

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by jlmac2001
For the gradient of phi(r)=xy, I got yi + xj. Is this right? [/B]
Yes.

Tom Mattson
Staff Emeritus
Gold Member

Originally posted by jlmac2001
how will I plot it. Do i have to solve the eequation at each of those points and plot the answer that I get?
No, it's not that involved. For each of the 4 points, you plug in the values of x and y (edit: plug them into the gradient). From those, you will get 4 vectors, which you need to sketch on the graph.

is this right ?

Okay. So at (1,1) it would be i + j
at(-1, 1)= -i
at (1,-1) = i-j
at (-1,-1) = -i-j

How would I plot it?

Tom Mattson
Staff Emeritus
Gold Member

Originally posted by jlmac2001
Okay. So at (1,1) it would be i + j
Right.

at(-1, 1)= -i
at (1,-1) = i-j