Use the Divergence Theorem to compute the net outward flux of the field F = (x,yz) across the surface S, where S is the sphere {(x.y.z): x +y +z = 16}. %3D 22.2. The net outward flux across the surface is 0. (Type an exact answer, using 1 as needed.)

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (2x,3y,2z) across the…

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A: The solution is given as

Q: Use Gauss' Divergent Theorem to calculate F. dS. where F = (sin(y?) + a)i + ey?j – 2e*+cos² (au)k…

A: Gauss divergence theorem is used

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A: From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E…

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A: To calculate the net outward flux of the given vector field across the given surface

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A: The following formula from Green's theorem is used to find the outward flux, outwards flux=∮F·n…

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Q: Use the Divergence Theorem to compute the net outward flux of the following field across the given…

A: We will find out the required value.

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A: Calculate: F=∇f   =∂∂xx2+y2+z2-1/2,∂∂yx2+y2+z2-1/2,∂∂zx2+y2+z2-1/2   =-x2+y2+z2-3/2x,y,z

Q: Q3. Consider the vector of electric field E(x,y,z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

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Q: Consider the force field F = (y, –2x² y) in R². Suppose that an object moves along the parametrized…

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Q: Determine the total work, by Green's theorem, performed by the force F(x, y) = field, on a particle…

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Q: Use the Divergence Theorem to evaluate the flux of the field F(x, y, z) = (e²²,5y + sin (x² z), 8z +…

A: To find:- The flux of the field F through surface S Concept Used:- The flux of the field F through…

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Q: 12. Use a parameterization to find the flux across the surface cut from the cylinder x? + y? = 1 by…

A: Image is attached with detailed explanation.

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A: We need to find the outward flux ∬DF→.dD We can use divergence theorem which equates ∬DF→.dD with…

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A: Given:F=-3x,y,8zS=x,y,z:x2+y2+z2=6

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A: Image is attached with detailed solution.

Q: Use the Divergence Theorem tO compute the flux oT the field 1 25x cos z, 6xy ) out of the region E…

A: Given,       1z2+y2arc tanxz2+y2, 25xcosz, 6xy out of the region E that lies between the spheres…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (x,y,z) across the…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, 3y, - 3z) across…

A: Let's find.

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A: We will find out the required value.

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Q: find the surface integral of the field F over the portion of the given surface in the specified…

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