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

## 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.03+1.29z)\rho ^{2}{\hat {\rho }}+8.35z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.03+1.29z)\rho ^{2}{\hat {\rho }}+8.35z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.03+1.29z)\rho ^{2}{\hat {\rho }}+8.35z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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

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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.74+1.27z)\rho ^{3}{\hat {\rho }}+9.08z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.74+1.27z)\rho ^{3}{\hat {\rho }}+9.08z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.74+1.27z)\rho ^{3}{\hat {\rho }}+9.08z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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

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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.48+2.38z)\rho ^{3}{\hat {\rho }}+8.41z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.48+2.38z)\rho ^{3}{\hat {\rho }}+8.41z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.48+2.38z)\rho ^{3}{\hat {\rho }}+8.41z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
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