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

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

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