- #1
physics_197
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Homework Statement
T(x,y,z) = -ln(x^2+y^2+z^2), F = -grad(T); S is the sphere x^2+y^2+z^2=a^2
Homework Equations
The Attempt at a Solution
Given:
F = (2/a^2) <x,y,z>
and the sphere x^2+y^2+z^2 = a^2
F (dot) n = (2/a^2) <x,y,z> (dot) (x/z,y/z,1)
In the end I get:
the double integral of: 2(a^2 - x^2 - y^2)^-0.5
Changing to polar coords I get:
2r / (a^2-r^2 ) drd(theta)
with limits: 0 < r < a and 0 < theta < 2pi
Once I solve it, I get an answer of: 4(pi)a, but the answer in the back is 8(pi)a
Is the answer in the back wrong? or did I make a mistake somewhere.