Question 1

Choose the INCORRECT statement:

Accepted Answer

A)  Gauss' law can be derived from Coulomb's law 
B)  Gauss' law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface 
C)  Coulomb's law can be derived from Gauss' law and symmetry 
D)  Gauss' law applies to a closed surface of any shape 
E)  According to Gauss' law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the surface 
A)  Gauss' law can be derived from Coulomb's law 
B)  Gauss' law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface 
C)  Coulomb's law can be derived from Gauss' law and symmetry 
D)  Gauss' law applies to a closed surface of any shape 
E)  According to Gauss' law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the surface

Question 2

Charge is distributed uniformly along a long straight wire. The electric field 2 cm from the wire is 20 N/C. The electric field 4 cm from the wire is:

Accepted Answer

A)  120 N/C 
B)  80 N/C 
C)  40 N/C 
D)  10 N/C 
E)  5 N/C 
A)  120 N/C 
B)  80 N/C 
C)  40 N/C 
D)  10 N/C 
E)  5 N/C

Question 3

The outer surface of the cardboard center of a paper towel roll:

Accepted Answer

A)  is a possible Gaussian surface 
B)  cannot be a Gaussian surface because it encloses no charge 
C)  cannot be a Gaussian surface since it is an insulator 
D)  cannot be a Gaussian surface since it is not closed 
E)  none of the above 
A)  is a possible Gaussian surface 
B)  cannot be a Gaussian surface because it encloses no charge 
C)  cannot be a Gaussian surface since it is an insulator 
D)  cannot be a Gaussian surface since it is not closed 
E)  none of the above

Question 4

Gauss's law:

Accepted Answer

A)  can always be used to calculate the electric field. 
B)  relates the electric field throughout space to the charges distributed through that space. 
C)  only applies to point charges. 
D)  relates the electric field at points on a closed surface to the net charge enclosed by that surface. 
E)  relates the surface charge density to the electric field. 
A)  can always be used to calculate the electric field. 
B)  relates the electric field throughout space to the charges distributed through that space. 
C)  only applies to point charges. 
D)  relates the electric field at points on a closed surface to the net charge enclosed by that surface. 
E)  relates the surface charge density to the electric field.

Question 5

A point charge is placed at the center of a spherical Gaussian surface. The electric flux $\phi$E is changed if:

Accepted Answer

A)  the sphere is replaced by a cube of the same volume 
B)  the sphere is replaced by a cube of one-tenth the volume 
C)  the point charge is moved off center (but still inside the original sphere) 
D)  the point charge is moved to just outside the sphere 
E)  a second point charge is placed just outside the sphere 
A)  the sphere is replaced by a cube of the same volume 
B)  the sphere is replaced by a cube of one-tenth the volume 
C)  the point charge is moved off center (but still inside the original sphere) 
D)  the point charge is moved to just outside the sphere 
E)  a second point charge is placed just outside the sphere

Question 6

A long line of charge with λℓ charge per unit length runs along the cylindrical axis of a cylindrical conducting shell which carries a charge per unit length of $\lambda$c. The charge per unit length on the inner and outer surfaces of the shell, respectively are:

Accepted Answer

A)  λℓ and $\lambda$c 
B)  −λℓ and $\lambda$c + λℓ 
C)  −λℓ and $\lambda$c - λℓ 
D)  λℓ + $\lambda$c and $\lambda$c - λℓ 
E)  λℓ - $\lambda$c and $\lambda$c + λℓ 
A)  λℓ and $\lambda$c 
B)  −λℓ and $\lambda$c + λℓ 
C)  −λℓ and $\lambda$c - λℓ 
D)  λℓ + $\lambda$c and $\lambda$c - λℓ 
E)  λℓ - $\lambda$c and $\lambda$c + λℓ

Question 7

To calculate the flux through a curved surface,

Accepted Answer

A)  the area vector has to be perpendicular to the surface somewhere 
B)  you must divide the surface into pieces that are tiny enough to be almost flat 
C)  the surface must be spherical 
D)  the surface cannot be curved very much; then you can treat it as though it were flat 
E)  actually the flux through a curved surface cannot be calculated. 
A)  the area vector has to be perpendicular to the surface somewhere 
B)  you must divide the surface into pieces that are tiny enough to be almost flat 
C)  the surface must be spherical 
D)  the surface cannot be curved very much; then you can treat it as though it were flat 
E)  actually the flux through a curved surface cannot be calculated.

Question 8

A 300-N/C uniform electric field points perpendicularly toward the left face of a large neutral conducting sheet. The area charge density on the left and right faces, respectively, are:

Accepted Answer

A)  -2.7 *10-9 C/m2; +2.7 *10-9 C/m 2 
B)  +2.7 *10-9 C/m2; -2.7 * 10-9 C/m 2 
C)  -5.3 *10-9 C/m2; +5.3 *10-9 C/m 2 
D)  +5.3 * 10-9 C/m2; -5.3 *10-9 C/m 2 
E)  0 C/m2; 0 C/m2 
A)  -2.7 *10-9 C/m2; +2.7 *10-9 C/m 2 
B)  +2.7 *10-9 C/m2; -2.7 * 10-9 C/m 2 
C)  -5.3 *10-9 C/m2; +5.3 *10-9 C/m 2 
D)  +5.3 * 10-9 C/m2; -5.3 *10-9 C/m 2 
E)  0 C/m2; 0 C/m2

Question 9

The area vector for a flat surface:

Accepted Answer

A)  is parallel to the surface and has a magnitude equal to the length of a side of the surface. 
B)  is perpendicular to the surface and has a magnitude equal to the length of a side of the surface. 
C)  is parallel to the surface and has a magnitude equal to the area of the surface. 
D)  is perpendicular to the surface and has a magnitude equal to the area of the surface. 
E)  none of the above. 
A)  is parallel to the surface and has a magnitude equal to the length of a side of the surface. 
B)  is perpendicular to the surface and has a magnitude equal to the length of a side of the surface. 
C)  is parallel to the surface and has a magnitude equal to the area of the surface. 
D)  is perpendicular to the surface and has a magnitude equal to the area of the surface. 
E)  none of the above.

Question 10

The electric flux Φ through a surface:

Accepted Answer

A)  is the amount of electric field piercing the surface. 
B)  is the electric field multiplied by the area. 
C)  does not depend on the area involved. 
D)  is the line integral of the electric field around the edge of the surface. 
E)  is the amount of electric field skimming along the surface. 
A)  is the amount of electric field piercing the surface. 
B)  is the electric field multiplied by the area. 
C)  does not depend on the area involved. 
D)  is the line integral of the electric field around the edge of the surface. 
E)  is the amount of electric field skimming along the surface.

Question 11

The table below gives the electric flux through the ends and round surfaces of four Gaussian surfaces in the form of cylinders. Rank the cylinders according to the charge inside, from the most negative to the most positive.

Accepted Answer

A)  1, 2, 3, 4 
B)  4, 3, 2, 1 
C)  3, 4, 2, 1 
D)  3, 1, 4, 2 
E)  4, 3, 1, 2 
A)  1, 2, 3, 4 
B)  4, 3, 2, 1 
C)  3, 4, 2, 1 
D)  3, 1, 4, 2 
E)  4, 3, 1, 2

Question 12

10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3 C is placed at the center of the cavity. The net charge on the inner surface of the shell is:

Accepted Answer

A)  -7 C 
B)  -3 C 
C)  0 C 
D)  +3 C 
E)  +7 C 
A)  -7 C 
B)  -3 C 
C)  0 C 
D)  +3 C 
E)  +7 C

Question 13

A point particle with charge q is at the center of a Gaussian surface in the form of a cube. The electric flux through any one face of the cube is:

Accepted Answer

A)  q/$\varepsilon$0 
B)  q/4 $\pi$$\varepsilon$0 
C)  q/4$\varepsilon$0 
D)  q/6$\varepsilon$0 
E)  q/16$\varepsilon$0 
A)  q/$\varepsilon$0 
B)  q/4 $\pi$$\varepsilon$0 
C)  q/4$\varepsilon$0 
D)  q/6$\varepsilon$0 
E)  q/16$\varepsilon$0

Question 14

Two large insulating parallel plates carry positive charge of equal magnitude that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.

Accepted Answer

A)  1, 2, 3, 4, 5 
B)  5, 4, 3, 2, 1 
C)  1 and 4 and 5 tie, then 2 and 3 tie 
D)  2 and 3 tie, then 1 and 4 tie, then 5 
E)  2 and 3 tie, then 1 and 4 and 5 tie 
A)  1, 2, 3, 4, 5 
B)  5, 4, 3, 2, 1 
C)  1 and 4 and 5 tie, then 2 and 3 tie 
D)  2 and 3 tie, then 1 and 4 tie, then 5 
E)  2 and 3 tie, then 1 and 4 and 5 tie

Question 15

Two large conducting parallel plates carry charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.

Accepted Answer

A)  1, 2, 3, 4, 5 
B)  5, 4, 3, 2, 1 
C)  1 and 4 and 5 tie, then 2 and 3 tie 
D)  2 and 3 tie, then 1 and 4 tie, then 5 
E)  2 and 3 tie, then 1 and 4 and 5 tie 
A)  1, 2, 3, 4, 5 
B)  5, 4, 3, 2, 1 
C)  1 and 4 and 5 tie, then 2 and 3 tie 
D)  2 and 3 tie, then 1 and 4 tie, then 5 
E)  2 and 3 tie, then 1 and 4 and 5 tie

Question 16

Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux through the outer surface of the shell is:

Accepted Answer

A)  0 
B)  Q/$\varepsilon$0 
C)  2Q/$\varepsilon$0 
D)  Q/4$\varepsilon$0 
E)  Q/2 $\pi$$\varepsilon$0 
A)  0 
B)  Q/$\varepsilon$0 
C)  2Q/$\varepsilon$0 
D)  Q/4$\varepsilon$0 
E)  Q/2 $\pi$$\varepsilon$0

Question 17

A cylindrical wastepaper basket with a 0.15-m radius opening is in a uniform electric field of 300 N/C, perpendicular to the opening. The total flux through the sides and bottom is:

Accepted Answer

A)  0 N.m2/C 
B)  4.2 N.m2/C 
C)  21 N.m2/C 
D)  280 N.m2/C 
E)  can't tell without knowing the areas of the sides and bottom 
A)  0 N.m2/C 
B)  4.2 N.m2/C 
C)  21 N.m2/C 
D)  280 N.m2/C 
E)  can't tell without knowing the areas of the sides and bottom

Question 18

Which statement is correct?

Accepted Answer

A)  The flux through a closed surface is always positive. 
B)  The flux through a closed surface is always negative. 
C)  The sign of the flux through a closed surface depends on an arbitrary choice of sign for the surface vector. 
D)  Inward flux through a closed surface is negative and outward flux is positive. 
E)  Inward flux through a closed surface is positive and outward flux is negative. 
A)  The flux through a closed surface is always positive. 
B)  The flux through a closed surface is always negative. 
C)  The sign of the flux through a closed surface depends on an arbitrary choice of sign for the surface vector. 
D)  Inward flux through a closed surface is negative and outward flux is positive. 
E)  Inward flux through a closed surface is positive and outward flux is negative.

Exam 23: Gauss Law

Choose the INCORRECT statement:

Charge is distributed uniformly along a long straight wire. The electric field 2 cm from the wire is 20 N/C. The electric field 4 cm from the wire is:

The outer surface of the cardboard center of a paper towel roll:

Gauss's law:

A point charge is placed at the center of a spherical Gaussian surface. The electric flux ϕ\phiϕ E is changed if:

A long line of charge with λℓ charge per unit length runs along the cylindrical axis of a cylindrical conducting shell which carries a charge per unit length of λ\lambdaλ c. The charge per unit length on the inner and outer surfaces of the shell, respectively are:

To calculate the flux through a curved surface,

A 300-N/C uniform electric field points perpendicularly toward the left face of a large neutral conducting sheet. The area charge density on the left and right faces, respectively, are:

The area vector for a flat surface:

The electric flux Φ through a surface:

The table below gives the electric flux through the ends and round surfaces of four Gaussian surfaces in the form of cylinders. Rank the cylinders according to the charge inside, from the most negative to the most positive.

10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3 C is placed at the center of the cavity. The net charge on the inner surface of the shell is:

A point particle with charge q is at the center of a Gaussian surface in the form of a cube. The electric flux through any one face of the cube is:

Two large insulating parallel plates carry positive charge of equal magnitude that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.

Two large conducting parallel plates carry charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.

Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux through the outer surface of the shell is:

A cylindrical wastepaper basket with a 0.15-m radius opening is in a uniform electric field of 300 N/C, perpendicular to the opening. The total flux through the sides and bottom is:

Which statement is correct?

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A point charge is placed at the center of a spherical Gaussian surface. The electric flux $\phi$ _E is changed if:

A long line of charge with λ_ℓ charge per unit length runs along the cylindrical axis of a cylindrical conducting shell which carries a charge per unit length of $\lambda$ _c. The charge per unit length on the inner and outer surfaces of the shell, respectively are: