The discussion revolves around finding a vector F based on a visual representation provided in an image link. The problem appears to involve concepts related to vector fields and their magnitudes in a two-dimensional plane, particularly in relation to the z-axis.
The conversation is ongoing, with participants providing feedback on each other's attempts. Some guidance has been offered regarding the necessary adjustments to the magnitude of the vector, but no consensus has been reached on a final expression for F.
There is a recurring emphasis on the relationship between the vector's components and their magnitudes in relation to the distance from the z-axis, with specific reference to the factor of 4 in the magnitude. Participants are also grappling with the implications of their mathematical manipulations.
-EquinoX- said:Homework Statement
http://img245.imageshack.us/img245/7535/38187200.th.jpg
I need to find F from the picture above
Homework Equations
The Attempt at a Solution
My answer so far is:
\frac{-y}{(x^2+y^2)} \vec{i} + \frac{x}{(x^2+y^2)} \vec{j}
is this correct?
benorin said:No. The magnitude is at a distance r from the z-axis should be 4r. recall that r=\sqrt{x^2+y^2}. Note that your "answer so far" has the properties depicted except that it has magnitude 1/r at a distance r from the z-axis.
As benorin said, your first attempt had magnitude 1/r and it should be 4r. For your second attempt you just divided by 4. That makes the magnitude 1/4r, not 4r. You need to multiply your first answer by 4r2= 4(x2+ y2).-EquinoX- said:so it should then be:
\frac{-y}{4(x^2+y^2)} \vec{i} + \frac{x}{4(x^2+y^2)} \vec{j}