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Finding F

  • Thread starter -EquinoX-
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  • #1
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Homework Statement



http://img245.imageshack.us/img245/7535/38187200.th.jpg [Broken]

I need to find F from the picture above

Homework Equations





The Attempt at a Solution



My answer so far is:

[tex] \frac{-y}{(x^2+y^2)} \vec{i} + \frac{x}{(x^2+y^2)} \vec{j} [/tex]

is this correct?
 
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Answers and Replies

  • #2
benorin
Homework Helper
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No. The magnitude is at a distance r from the z-axis should be 4r. recall that [tex]r=\sqrt{x^2+y^2}[/tex]. 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.
 
  • #3
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so it should then be:

[tex] \frac{-y}{4(x^2+y^2)} \vec{i} + \frac{x}{4(x^2+y^2)} \vec{j} [/tex]
 
  • #4
benorin
Homework Helper
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Does [tex]\sqrt{\left(\frac{-y}{4(x^2+y^2)}\right)^2 + \left(\frac{x}{4(x^2+y^2)}\right)^2}=4\sqrt{x^2+y^2}[/tex]?

No. Look, [tex]-y\vec{i}+x\vec{j}[/tex] is a vector field whose vectors point in all the right directions, make them the proper length.
 
  • #5
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I have no clue.... I've tried [tex] -4y\vec{i} + 4x\vec{j} [/tex] and it seems to be wrong as well
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,793
922

Homework Statement



http://img245.imageshack.us/img245/7535/38187200.th.jpg [Broken]

I need to find F from the picture above

Homework Equations





The Attempt at a Solution



My answer so far is:

[tex] \frac{-y}{(x^2+y^2)} \vec{i} + \frac{x}{(x^2+y^2)} \vec{j} [/tex]

is this correct?
No. The magnitude is at a distance r from the z-axis should be 4r. recall that [tex]r=\sqrt{x^2+y^2}[/tex]. 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.
so it should then be:

[tex] \frac{-y}{4(x^2+y^2)} \vec{i} + \frac{x}{4(x^2+y^2)} \vec{j} [/tex]
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).
 
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  • #7
564
0
so it's just simply:

[tex]-4y\vec{i} + 4x\vec{j}[/tex]
 

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