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

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pe19surfaceIntegralsCalculus A

1. 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

2. 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

3. 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

Your score is 0 / 0

pe19surfaceIntegralsCalculus B

1. 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

2. 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

3. 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

Your score is 0 / 0

pe19surfaceIntegralsCalculus C

1. 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

2. 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

3. 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

Your score is 0 / 0
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