Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first octant in the direction away from the origin.
Added by Roger O.
Step 1
The surface is the portion of the sphere \(x^2 + y^2 + z^2 = a^2\) in the first octant. The first octant is defined by \(x \geq 0\), \(y \geq 0\), and \(z \geq 0\). Show more…
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In Exercises $21-26,$ find the flux of the field $\mathbf{F}$ across the portion of the sphere $x^{2}+y^{2}+z^{2}=a^{2}$ in the first octant in the direction away from the origin. $$ \begin{array}{c}{\mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}} \\ {x \mathbf{i}+y \mathbf{j}+z \mathbf{k}}\end{array} $$
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In Exercises $21-26,$ find the flux of the field $\mathbf{F}$ across the portion of the sphere $x^{2}+y^{2}+z^{2}=a^{2}$ in the first octant in the direction away from the origin. $$ \mathbf{F}(x, y, z)=z x \mathbf{i}+z y \mathbf{j}+z^{2} \mathbf{k} $$
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