Quizbank/University Physics Semester 2/T2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

a) 8.545E+01 V·m

b) 9.400E+01 V·m

c) 1.034E+02 V·m

d) 1.137E+02 V·m

e) 1.251E+02 V·m

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.8 m. The other four surfaces are rectangles in y=y₀=1.2 m, y=y₁=5.9 m, z=z₀=1.3 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 8.5m² ,and those in the zx plane have area 7.0m². An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.777E+01 N·m²/C

b) 5.254E+01 N·m²/C

c) 5.780E+01 N·m²/C

d) 6.358E+01 N·m²/C

e) 6.993E+01 N·m²/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.0 m. The other four surfaces are rectangles in y=y₀=1.8 m, y=y₁=4.2 m, z=z₀=1.3 m, and z=z₁=5.8 m. The surfaces in the yz plane each have area 11.0m². Those in the xy plane have area 4.8m² ,and those in the zx plane have area 9.0m². An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 4.125E+01 N·m²/C

b) 4.537E+01 N·m²/C

c) 4.991E+01 N·m²/C

d) 5.490E+01 N·m²/C

e) 6.039E+01 N·m²/C

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.1 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.606E+01 N·m²/C

b) 6.167E+01 N·m²/C

c) 6.784E+01 N·m²/C

d) 7.462E+01 N·m²/C

e) 8.208E+01 N·m²/C

5) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
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) 6.69E+03

b) 8.10E+03

c) 9.81E+03

d) 1.19E+04

e) 1.44E+04

6) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
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) 4.593E+03

b) 5.564E+03

c) 6.741E+03

d) 8.167E+03

e) 9.894E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

e) none of these are correct

8) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

e) none of these are correct

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) none of these are correct

b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

1) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

b) none of these are correct

c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

2) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

c) none of these are correct

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

c) none of these are correct

d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.7 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.3 m, z=z₀=1.8 m, and z=z₁=4.9 m. The surfaces in the yz plane each have area 8.1m². Those in the xy plane have area 7.0m² ,and those in the zx plane have area 8.4m². An electric field has the xyz components (0, 9.2, 7.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.364E+01 N·m²/C

b) 7.000E+01 N·m²/C

c) 7.700E+01 N·m²/C

d) 8.470E+01 N·m²/C

e) 9.317E+01 N·m²/C

5) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(1.93+2.31z)\rho ^{3}{\hat {\rho }}+7.21z^{2}{\hat {z}}}$
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) 5.40E+02

b) 6.55E+02

c) 7.93E+02

d) 9.61E+02

e) 1.16E+03

6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m

b) 2.871E+03 V·m

c) 3.158E+03 V·m

d) 3.474E+03 V·m

e) 3.822E+03 V·m

7) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
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) 4.593E+03

b) 5.564E+03

c) 6.741E+03

d) 8.167E+03

e) 9.894E+03

8) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

c) none of these are correct

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.1 m, and z=z₁=5.2 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.606E+01 N·m²/C

b) 6.167E+01 N·m²/C

c) 6.784E+01 N·m²/C

d) 7.462E+01 N·m²/C

e) 8.208E+01 N·m²/C

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.5 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.9 m, z=z₀=1.1 m, and z=z₁=5.3 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 8.8m² ,and those in the zx plane have area 10.0m². An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.439E+01 N·m²/C

b) 5.983E+01 N·m²/C

c) 6.581E+01 N·m²/C

d) 7.239E+01 N·m²/C

e) 7.963E+01 N·m²/C

1) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

c) none of these are correct

d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
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) 6.201E+02

b) 7.513E+02

c) 9.102E+02

d) 1.103E+03

e) 1.336E+03

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.1 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=5.3 m, z=z₀=1.1 m, and z=z₁=4.3 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 8.8m² ,and those in the zx plane have area 6.7m². An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.924E+01 N·m²/C

b) 4.316E+01 N·m²/C

c) 4.748E+01 N·m²/C

d) 5.222E+01 N·m²/C

e) 5.745E+01 N·m²/C

4) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}}$
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) 4.69E+03

b) 5.69E+03

c) 6.89E+03

d) 8.35E+03

e) 1.01E+04

5) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

d) none of these are correct

e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m

b) 2.166E+02 V·m

c) 2.383E+02 V·m

d) 2.621E+02 V·m

e) 2.883E+02 V·m

8) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

d) none of these are correct

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.4 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=5.7 m, z=z₀=1.9 m, and z=z₁=5.4 m. The surfaces in the yz plane each have area 15.0m². Those in the xy plane have area 11.0m² ,and those in the zx plane have area 8.4m². An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.012E+01 N·m²/C

b) 2.213E+01 N·m²/C

c) 2.435E+01 N·m²/C

d) 2.678E+01 N·m²/C

e) 2.946E+01 N·m²/C

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.5 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=5.3 m, z=z₀=1.3 m, and z=z₁=4.3 m. The surfaces in the yz plane each have area 12.0m². Those in the xy plane have area 10.0m² ,and those in the zx plane have area 7.5m². An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.614E+01 N·m²/C

b) 7.275E+01 N·m²/C

c) 8.003E+01 N·m²/C

d) 8.803E+01 N·m²/C

e) 9.683E+01 N·m²/C

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

a) 3.337E+03 V·m

b) 3.670E+03 V·m

c) 4.037E+03 V·m

d) 4.441E+03 V·m

e) 4.885E+03 V·m

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.7 m. The other four surfaces are rectangles in y=y₀=1.9 m, y=y₁=4.3 m, z=z₀=1.7 m, and z=z₁=5.7 m. The surfaces in the yz plane each have area 9.6m². Those in the xy plane have area 4.1m² ,and those in the zx plane have area 6.8m². An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 7.876E+01 N·m²/C

b) 8.664E+01 N·m²/C

c) 9.531E+01 N·m²/C

d) 1.048E+02 N·m²/C

e) 1.153E+02 N·m²/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.0 m. The other four surfaces are rectangles in y=y₀=1.8 m, y=y₁=5.8 m, z=z₀=1.9 m, and z=z₁=5.9 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 8.0m² ,and those in the zx plane have area 8.0m². An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.662E+01 N·m²/C

b) 4.028E+01 N·m²/C

c) 4.430E+01 N·m²/C

d) 4.873E+01 N·m²/C

e) 5.361E+01 N·m²/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=2 nC·m^-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C

b) 1.522E+02 N/C

c) 1.674E+02 N/C

d) 1.841E+02 N/C

e) 2.025E+02 N/C

5) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.44+2.86z)\rho ^{2}{\hat {\rho }}+7.42z^{3}{\hat {z}}}$
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) 9.41E+03

b) 1.14E+04

c) 1.38E+04

d) 1.67E+04

e) 2.03E+04

6) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
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) 4.489E+02

b) 5.438E+02

c) 6.589E+02

d) 7.983E+02

e) 9.671E+02

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=H\rho z}$

b) ${\displaystyle \varepsilon _{0}E=\rho z}$

c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

d) none of these are correct

e) ${\displaystyle \varepsilon _{0}E=H\rho }$

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct

b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

9) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

c) none of these are correct

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

e) none of these are correct

1) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.04+1.66z)\rho ^{2}{\hat {\rho }}+7.54z^{2}{\hat {z}}}$
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) 8.528E+02

b) 1.033E+03

c) 1.252E+03

d) 1.516E+03

e) 1.837E+03

2) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=3 nC·m^-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?

a) 4.874E+01 N/C

b) 5.362E+01 N/C

c) 5.898E+01 N/C

d) 6.488E+01 N/C

e) 7.137E+01 N/C

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=H\rho z}$

b) ${\displaystyle \varepsilon _{0}E=\rho z}$

c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

d) ${\displaystyle \varepsilon _{0}E=H\rho }$

e) none of these are correct

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.8 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=4.9 m, z=z₀=1.3 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 6.8m² ,and those in the zx plane have area 7.7m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.898E+01 N·m²/C

b) 7.588E+01 N·m²/C

c) 8.347E+01 N·m²/C

d) 9.181E+01 N·m²/C

e) 1.010E+02 N·m²/C

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m

b) 3.771E+03 V·m

c) 4.149E+03 V·m

d) 4.564E+03 V·m

e) 5.020E+03 V·m

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

d) none of these are correct

e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

7) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.6 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.4 m, z=z₀=1.4 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 9.6m² ,and those in the zx plane have area 11.0m². An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 8.921E+01 N·m²/C

b) 9.813E+01 N·m²/C

c) 1.079E+02 N·m²/C

d) 1.187E+02 N·m²/C

e) 1.306E+02 N·m²/C

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

b) none of these are correct

c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

e) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

10) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}}$
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) 4.63E+03

b) 5.61E+03

c) 6.79E+03

d) 8.23E+03

e) 9.97E+03

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.5 m, y=y₁=5.8 m, z=z₀=1.7 m, and z=z₁=5.8 m. The surfaces in the yz plane each have area 18.0m². Those in the xy plane have area 5.6m² ,and those in the zx plane have area 5.3m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.712E+01 N·m²/C

b) 4.083E+01 N·m²/C

c) 4.491E+01 N·m²/C

d) 4.940E+01 N·m²/C

e) 5.434E+01 N·m²/C

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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(1.89+1.31z)\rho ^{3}{\hat {\rho }}+8.35z^{2}{\hat {z}}}$
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) 9.41E+02

b) 1.14E+03

c) 1.38E+03

d) 1.67E+03

e) 2.03E+03

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

a) 2.210E+04 V·m

b) 2.431E+04 V·m

c) 2.674E+04 V·m

d) 2.941E+04 V·m

e) 3.235E+04 V·m

4) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(1.93+2.31z)\rho ^{3}{\hat {\rho }}+7.21z^{2}{\hat {z}}}$
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) 6.731E+02

b) 8.154E+02

c) 9.879E+02

d) 1.197E+03

e) 1.450E+03

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

d) none of these are correct

e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

b) none of these are correct

c) ${\displaystyle \varepsilon _{0}E=\rho z}$

d) ${\displaystyle \varepsilon _{0}E=H\rho }$

e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.9 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=5.9 m, z=z₀=1.3 m, and z=z₁=5.3 m. The surfaces in the yz plane each have area 17.0m². Those in the xy plane have area 12.0m² ,and those in the zx plane have area 12.0m². An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 1.737E+01 N·m²/C

b) 1.910E+01 N·m²/C

c) 2.101E+01 N·m²/C

d) 2.311E+01 N·m²/C

e) 2.543E+01 N·m²/C

8) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.5 (r≤R) where a=3 nC·m^-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

a) 2.039E+01 N/C

b) 2.243E+01 N/C

c) 2.467E+01 N/C

d) 2.714E+01 N/C

e) 2.985E+01 N/C

9) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) none of these are correct

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

b) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

e) none of these are correct

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m

b) 2.274E+03 V·m

c) 2.501E+03 V·m

d) 2.752E+03 V·m

e) 3.027E+03 V·m

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.1 m, y=y₁=5.7 m, z=z₀=1.8 m, and z=z₁=4.5 m. The surfaces in the yz plane each have area 12.0m². Those in the xy plane have area 6.0m² ,and those in the zx plane have area 3.5m². An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 9.823E+00 N·m²/C

b) 1.080E+01 N·m²/C

c) 1.189E+01 N·m²/C

d) 1.307E+01 N·m²/C

e) 1.438E+01 N·m²/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.5 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=5.3 m, z=z₀=1.3 m, and z=z₁=4.3 m. The surfaces in the yz plane each have area 12.0m². Those in the xy plane have area 10.0m² ,and those in the zx plane have area 7.5m². An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 6.614E+01 N·m²/C

b) 7.275E+01 N·m²/C

c) 8.003E+01 N·m²/C

d) 8.803E+01 N·m²/C

e) 9.683E+01 N·m²/C

4) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.4 (r≤R) where a=2 nC·m^-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

a) 3.821E+02 N/C

b) 4.203E+02 N/C

c) 4.624E+02 N/C

d) 5.086E+02 N/C

e) 5.594E+02 N/C

5) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
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) 1.29E+03

b) 1.56E+03

c) 1.89E+03

d) 2.29E+03

e) 2.77E+03

6) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
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) 5.043E+02

b) 6.109E+02

c) 7.402E+02

d) 8.967E+02

e) 1.086E+03

7) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

b) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

c) none of these are correct

d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

8) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct

b) ${\displaystyle \varepsilon _{0}E=\rho z}$

c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

d) ${\displaystyle \varepsilon _{0}E=H\rho }$

e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

9) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

c) none of these are correct

d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

e) none of these are correct

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.0 m. The other four surfaces are rectangles in y=y₀=1.8 m, y=y₁=5.8 m, z=z₀=1.9 m, and z=z₁=5.9 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 8.0m² ,and those in the zx plane have area 8.0m². An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.662E+01 N·m²/C

b) 4.028E+01 N·m²/C

c) 4.430E+01 N·m²/C

d) 4.873E+01 N·m²/C

e) 5.361E+01 N·m²/C

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

b) none of these are correct

c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

d) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

3) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C

b) 2.501E+02 N/C

c) 2.751E+02 N/C

d) 3.026E+02 N/C

e) 3.329E+02 N/C

4) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=H\rho }$

b) ${\displaystyle \varepsilon _{0}E=H\rho z}$

c) ${\displaystyle \varepsilon _{0}E=\rho z}$

d) none of these are correct

e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

5) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
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) 1.59E+03

b) 1.93E+03

c) 2.34E+03

d) 2.83E+03

e) 3.43E+03

6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

a) 4.286E+03 V·m

b) 4.714E+03 V·m

c) 5.186E+03 V·m

d) 5.704E+03 V·m

e) 6.275E+03 V·m

7) A cylinder of radius, r=3, 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.68z)\rho ^{2}{\hat {\rho }}+8.83z^{3}{\hat {z}}}$
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) 4.593E+03

b) 5.564E+03

c) 6.741E+03

d) 8.167E+03

e) 9.894E+03

8) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

c) none of these are correct

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.3 m. The other four surfaces are rectangles in y=y₀=1.6 m, y=y₁=5.3 m, z=z₀=1.3 m, and z=z₁=5.6 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 4.8m² ,and those in the zx plane have area 5.6m². An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.074E+01 N·m²/C

b) 3.382E+01 N·m²/C

c) 3.720E+01 N·m²/C

d) 4.092E+01 N·m²/C

e) 4.501E+01 N·m²/C

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

d) none of these are correct

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.0 m. The other four surfaces are rectangles in y=y₀=1.8 m, y=y₁=5.8 m, z=z₀=1.9 m, and z=z₁=5.9 m. The surfaces in the yz plane each have area 16.0m². Those in the xy plane have area 8.0m² ,and those in the zx plane have area 8.0m². An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 3.662E+01 N·m²/C

b) 4.028E+01 N·m²/C

c) 4.430E+01 N·m²/C

d) 4.873E+01 N·m²/C

e) 5.361E+01 N·m²/C

2) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

d) none of these are correct

e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

a) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

b) none of these are correct

c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$

d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

e) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$

4) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) none of these are correct

b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$

d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=2.8 m. The other four surfaces are rectangles in y=y₀=1.7 m, y=y₁=4.5 m, z=z₀=1.5 m, and z=z₁=5.0 m. The surfaces in the yz plane each have area 9.8m². Those in the xy plane have area 7.8m² ,and those in the zx plane have area 9.8m². An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 5.978E+01 N·m²/C

b) 6.576E+01 N·m²/C

c) 7.233E+01 N·m²/C

d) 7.957E+01 N·m²/C

e) 8.752E+01 N·m²/C

6) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
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) 1.09E+03

b) 1.32E+03

c) 1.60E+03

d) 1.94E+03

e) 2.35E+03

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

a) 8.545E+01 V·m

b) 9.400E+01 V·m

c) 1.034E+02 V·m

d) 1.137E+02 V·m

e) 1.251E+02 V·m

8) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar^1.2 (r≤R) where a=2 nC·m^-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C

b) 2.501E+02 N/C

c) 2.751E+02 N/C

d) 3.026E+02 N/C

e) 3.329E+02 N/C

9) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
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) 5.043E+02

b) 6.109E+02

c) 7.402E+02

d) 8.967E+02

e) 1.086E+03

10) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=H\rho z}$

b) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

c) ${\displaystyle \varepsilon _{0}E=H\rho }$

d) ${\displaystyle \varepsilon _{0}E=\rho z}$

e) none of these are correct

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

a) 3.251E+01 N/C

b) 3.577E+01 N/C

c) 3.934E+01 N/C

d) 4.328E+01 N/C

e) 4.760E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m

b) 7.759E+03 V·m

c) 8.535E+03 V·m

d) 9.388E+03 V·m

e) 1.033E+04 V·m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.6 m. The other four surfaces are rectangles in y=y₀=1.3 m, y=y₁=4.4 m, z=z₀=1.4 m, and z=z₁=5.5 m. The surfaces in the yz plane each have area 13.0m². Those in the xy plane have area 5.0m² ,and those in the zx plane have area 6.6m². An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 2.756E+01 N·m²/C

b) 3.032E+01 N·m²/C

c) 3.335E+01 N·m²/C

d) 3.668E+01 N·m²/C

e) 4.035E+01 N·m²/C

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x₁=1.5 m. The other four surfaces are rectangles in y=y₀=1.4 m, y=y₁=4.9 m, z=z₀=1.1 m, and z=z₁=4.4 m. The surfaces in the yz plane each have area 12.0m². Those in the xy plane have area 5.3m² ,and those in the zx plane have area 5.0m². An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?

a) 7.793E+01 N·m²/C

b) 8.572E+01 N·m²/C

c) 9.429E+01 N·m²/C

d) 1.037E+02 N·m²/C

e) 1.141E+02 N·m²/C

5) 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,
 ${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
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) 4.489E+02

b) 5.438E+02

c) 6.589E+02

d) 7.983E+02

e) 9.671E+02