- #1
cos(e)
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Homework Statement
find the flux of the field F(vector) across the portion of the sphere x^2+y^2+z^2=a^2 in the first octant directed away from the origin
Homework Equations
F(x,y,z)=zk(hat)
The Attempt at a Solution
i used Flux=double integral over x-y plane F.n(unit normal)dsigma
where dsigma=abs(grad(g))/abs(grad(g).p(unit normal to surface))
i let g=x^2+y^2+z^2-a^2=0
and grad(g)=(2x,2y,2z)
p=n=(x,y,z)/sqrt(x^2+y^2+z^2)
and after some algebra i got:
double integral( (a^2-x^2-y^2)/a dA)
which i used polar co-ordinates
to get 1/a double integral( a^2-r^2)r dr dtheta
which gave me pi*a^3/8 yet the solutions in back of book is pi*a^3/6
Looks like iv made a simple error somewhere(iv looked like 3 times but can't find one), but i just need to check I am using the right method.
sorry bout the way i worte out the maths but I am unaware how to put it in nice maths form
Can any1 help please?
cheers,
cos(e)