Flux across a sphere Consider the radial field F = 〈 x , y , z 〉 and let S be the sphere of radius a centered at the origin. Compute the outward flux of F across S using the representation z = ± a 2 − x 2 − y 2 for the sphere (either symmetry or two surfaces must be used).
Flux across a sphere Consider the radial field F = 〈 x , y , z 〉 and let S be the sphere of radius a centered at the origin. Compute the outward flux of F across S using the representation z = ± a 2 − x 2 − y 2 for the sphere (either symmetry or two surfaces must be used).
Flux across a sphere Consider the radial field F = 〈x, y, z〉 and let S be the sphere of radius a centered at the origin. Compute the outward flux of F across S using the representation
z
=
±
a
2
−
x
2
−
y
2
for the sphere (either symmetry or two surfaces must be used).
A net is dipped in a river. Determine the
flow rate of water across the net if the
velocity vector field for the river is given
by v=(x-y,z+y+7,z2) and the net is
decribed by the equation y=1-x2-z2, y20,
and oriented in the positive y- direction.
(Use symbolic notation and fractions
where needed.)
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by
= (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y-
direction.
(Use symbolic notation and fractions where needed.)
V. dS =
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