Physics equations/19-Electric Potential and Electric Field/Q:SurfaceIntegralsCalculus

Equations for this quiz      Solutions (pdf)       /testbank/

pe19surfaceIntegralsCalculus A
{A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (2.03+1.29z)\rho^2\hat\rho +8.35z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.} -a) 1.315E+03 -b) 1.593E+03 -c) 1.930E+03 -d) 2.338E+03 +e) 2.833E+03 {A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis.  A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (2.03+1.29z)\rho^2\hat\rho +8.35z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{side}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over curved side surface of the cylinder.} -a) 3.443E+02 -b) 4.171E+02 -c) 5.053E+02 +d) 6.122E+02 -e) 7.417E+02 {A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (2.03+1.29z)\rho^2\hat\rho +8.35z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the entire surface of the cylinder.} -a) 2.94E+03 -b) 3.54E+03 -c) 4.27E+03 -d) 5.15E+03 +e) 6.28E+03

pe19surfaceIntegralsCalculus B
{A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (1.74+1.27z)\rho^3\hat\rho +9.08z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.} -a) 2.118E+02 -b) 2.567E+02 -c) 3.109E+02 -d) 3.767E+02 +e) 4.564E+02 {A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis.  A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (1.74+1.27z)\rho^3\hat\rho +9.08z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{side}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the curved side surface of the cylinder.} +a) 6.997E+02 -b) 8.477E+02 -c) 1.027E+03 -d) 1.244E+03 -e) 1.507E+03 {A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (1.74+1.27z)\rho^3\hat\rho +9.08z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the entire surface of the cylinder.} -a) 4.77E+02 -b) 5.78E+02 +c) 7.00E+02 -d) 8.48E+02 -e) 1.03E+03

pe19surfaceIntegralsCalculus C
{A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (2.48+2.38z)\rho^3\hat\rho +8.41z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.} -a) 2.377E+02 -b) 2.880E+02 -c) 3.489E+02 +d) 4.227E+02 -e) 5.122E+02 {A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis.  A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (2.48+2.38z)\rho^3\hat\rho +8.41z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{side}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the curved side surface of the cylinder.} +a) 9.973E+02 -b) 1.208E+03 -c) 1.464E+03 -d) 1.773E+03 -e) 2.149E+03 {A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (2.48+2.38z)\rho^3\hat\rho +8.41z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the entire surface of the cylinder.} +a) 9.97E+02 -b) 1.21E+03 -c) 1.46E+03 -d) 1.77E+03 -e) 2.15E+03