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2D 1- Let A = x²0²₂² + jag, taz and let 5 be a surface de yay by psh, aszab, cylindrical coordinates. a- Express A in b- Find &Aids S C- Find V.A in d. cylindrical coordinates- Find St. A dv where Vis the volume enclosed by s.

2D 1- Let A = x²0²₂² + jag, taz and let 5 be a surface de yay by psh, aszab, cylindrical coordinates. a- Express A in b- Find &Aids S C- Find V.A in d. cylindrical coordinates- Find St. A dv where Vis the volume enclosed by s.

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**Problem 1** Let \(\vec{A} = x^2 \hat{a}_x + y^2 \hat{a}_y + z^2 \hat{a}_z\) and let \(S\) be a surface defined by \(\rho \leq h\); \(a \leq z \leq b\). a. Express \(\vec{A}\) in cylindrical coordinates. b. Find \(\oint_S \vec{A} \cdot d\vec{s}\). c. Find \(\nabla \cdot \vec{A}\) in cylindrical coordinates. d. Find \(\int_V \nabla \cdot \vec{A} \, dv\) where \(V\) is the volume enclosed by \(S\).
Transcribed Image Text:**Problem 1** Let \(\vec{A} = x^2 \hat{a}_x + y^2 \hat{a}_y + z^2 \hat{a}_z\) and let \(S\) be a surface defined by \(\rho \leq h\); \(a \leq z \leq b\). a. Express \(\vec{A}\) in cylindrical coordinates. b. Find \(\oint_S \vec{A} \cdot d\vec{s}\). c. Find \(\nabla \cdot \vec{A}\) in cylindrical coordinates. d. Find \(\int_V \nabla \cdot \vec{A} \, dv\) where \(V\) is the volume enclosed by \(S\).
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