Question 1

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a +2.00-µC point charge placed at its center. Find the surface charge density
(a) on the inner surface of the shell.
(b) on the outer surface of the shell.

Accepted Answer

(a) -1590 ...

Question 2

Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 N/C at a point 4.10 m from the center of the shells. The outer surface of the larger shell has a radius of 3.75 m. If the inner shell contains an excess charge of -5.30 μC, find the amount of charge on the outer surface of the larger shell. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

Question 3

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is

Accepted Answer

A)   along a line between the lines closer to line #2 than line #1.
B)   at a point midway between the lines.
C)   along a line perpendicular to lines #1 and #2.
D)   along a line between the lines closer to line #1 than line #2.

Question 4

Under electrostatic conditions, the electric field just outside the surface of any charged conductor

Accepted Answer

A)   is always parallel to the surface.
B)   is always zero because the electric field is zero inside conductors.
C)   is always perpendicular to the surface of the conductor.
D)   is perpendicular to the surface of the conductor only if it is a sphere, a cylinder, or a flat sheet.
E)   can have nonzero components perpendicular to and parallel to the surface of the conductor.

Question 5

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries a net excess charge of -500 nC. A point charge of +300 nC is present at the center. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C)  The radial component of the electric field at a point that is 1.50 m from the center is closest to 9 N ∙ m2/C)  The radial component of the electric field at a point that is 1.50 m from the center is closest to   A)  +1200 N/C. B)  +2000 N/C. C)  -800 N/C. D)  -1600 N/C. E)  -2000 N/C." class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A)   +1200 N/C.
B)   +2000 N/C.
C)   -800 N/C.
D)   -1600 N/C.
E)   -2000 N/C.

Question 6

A cone is resting on a tabletop as shown in the figure with its face horizontal. A uniform electric field of magnitude 4550 N/C points vertically upward. How much electric flux passes through the sloping side surface area of the cone?

Accepted Answer

6.36 N ∙ m²/C

Question 7

Two concentric spheres are shown in the figure. The inner sphere is a solid nonconductor and carries a charge of +5.00 µC uniformly distributed over its outer surface. The outer sphere is a conducting shell that carries a net charge of -8.00 µC. No other charges are present. The radii shown in the figure have the values R1 = 10.0 cm, R2 = 20.0 cm, and R3 = 30.0 cm. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)
(a) Find the total excess charge on the inner and outer surfaces of the conducting sphere.
(b) Find the magnitude and direction of the electric field at the following distances r from the center of the inner sphere: (i) r = 9.5 cm, (ii) r = 15.0 cm, (iii) r = 27.0 cm, (iv) r = 35.0 cm.

Accepted Answer

(a) -5.00 µC (inner surface), ...

Question 8

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distance r1 (r1 < R)  from the center of the sphere, the electric field has magnitude E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R, the magnitude of the electric field at the same distance r1 from the center would be equal to

Accepted Answer

A)   E/8.
B)   E/2.
C)   2E.
D)   8E.
E)   E.

Question 9

A charge of 1.0 × 10-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)   0.11 N ∙ m2/C
B)   8.9 N ∙ m2/C
C)   0.028π N ∙ m2/C
D)   It cannot be determined without knowing the radius of the sphere.

Question 10

A huge (essentially infinite)  horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces. The upper face carries +95.0 nC/m2 while the lower face carries -25.0 nC/ m2. What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)   0.00 N/C
B)   3.95 × 103 N/C
C)   6.78 × 103 N/C
D)   7.91 × 103 N/C
E)   1.36 × 104 N/C

Question 11

Charge is distributed uniformly throughout a large insulating cylinder of radius R. The charge per unit length in the cylindrical volume is λ.
(a) Use Gauss's law to find the magnitude of the electric field at a distance r from the central axis of the cylinder for r < R. Your answer should be in terms of r, R, λ, ε₀ , and π.
(b) Check the reasonableness of your answer by evaluating it at the surface of the cylinder.

Accepted Answer

(a) E =

(b) At r =...

Question 12

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

Accepted Answer

A)   Gauss's law is valid only for symmetric charge distributions, such as spheres and cylinders.
B)   If there is no charge inside of a Gaussian surface, the electric field must be zero at points of that surface.
C)   Only charge enclosed within a Gaussian surface can produce an electric field at points on that surface.
D)   If a Gaussian surface is completely inside an electrostatic conductor, the electric field must always be zero at all points on that surface.
E)   The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface, not on its size or shape.

Question 13

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC. A point charge of +300 nC is present at the center. The surface charge density on the inner spherical surface is closest to -8 C/m2. C)  +6.0 × 10-8 C/ m2. D)  -4.0 × 10-8 C/ m2. E)  -6.0 × 10-8 C/ m2." class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A)   zero.
B)   +4.0 × 10-8 C/m2.
C)   +6.0 × 10-8 C/ m2.
D)   -4.0 × 10-8 C/ m2.
E)   -6.0 × 10-8 C/ m2.

Question 14

The graph in the figure shows the electric field strength (not the field lines)  as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

Accepted Answer

A)   a positively charged conducting sphere within another positively charged conducting sphere
B)   a positively charged conducting sphere within an uncharged conducting sphere
C)   a solid nonconducting sphere, uniformly charged throughout its volume, inside of a positively charged conducting sphere
D)   a positively charged nonconducting thin-walled spherical shell inside of a positively charged conducting sphere
E)   a positively charged nonconducting thin-walled spherical shell inside of another positively charged nonconducting thin-walled spherical shell

Question 15

A nonconducting spherical shell of inner radius R₁ and outer radius R₂ contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R₁, R₂, r, ε₀ , and π.
(a) r 1
(b) R1 2
(c) r > R2

Accepted Answer

(a) E = 0 
(b) E =   
(c) E =

Question 16

At a distance D from a very long (essentially infinite)  uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?

Accepted Answer

A)   2D
B)    D
C)   D/ 
D)   D/2
E)   D/4

Question 17

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?

Accepted Answer

A)   3.5 cm only
B)   4.9 cm only
C)   3.5 cm and 9.9 cm
D)   3.5 cm and 4.9 cm
E)   9.9 cm only

Question 18

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field -12 C2/N ∙ m2)  A)  5.52 × 105 N ∙ m2/C B)  1.13 × 105 N ∙ m2/C C)  2.26 × 105 N ∙ m2/C D)  zero" class="answers-bank-image d-inline" rel="preload" > = (100 N/C)  î. Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)   5.52 × 105 N ∙ m2/C
B)   1.13 × 105 N ∙ m2/C
C)   2.26 × 105 N ∙ m2/C
D)   zero

Question 19

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

Accepted Answer

A)   0.11 m
B)   0.13 m
C)   0.15 m
D)   0.17 m
E)   at no other point A

Question 20

A spherical, non-conducting shell of inner radius r1 = 10 cm and outer radius r2 = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell. What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)   5.75 × 103 N/C
B)   zero
C)   2.87 × 106 N/C
D)   5.75 × 106 N/C
E)   2.87 × 103 N/C

Exam 21: Gausss Law

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a +2.00-µC point charge placed at its center. Find the surface charge density (a) on the inner surface of the shell. (b) on the outer surface of the shell.

Correct Answer
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(a) -1590 ...
View Answer

Correct Answer
verified

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is

Correct Answer
verified

Under electrostatic conditions, the electric field just outside the surface of any charged conductor

Correct Answer
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Correct Answer
verified

A cone is resting on a tabletop as shown in the figure with its face horizontal. A uniform electric field of magnitude 4550 N/C points vertically upward. How much electric flux passes through the sloping side surface area of the cone?

Correct Answer
verified
6.36 N ∙ m²/C

Correct Answer
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(a) -5.00 µC (inner surface), ...
View Answer

Correct Answer
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A charge of 1.0 × 10^-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Correct Answer
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Correct Answer
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Correct Answer
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(a) E =
(b) At r =...
View Answer

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

Correct Answer
verified

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC. A point charge of +300 nC is present at the center. The surface charge density on the inner spherical surface is closest to

Correct Answer
verified

The graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

Correct Answer
verified

Correct Answer
verified
(a) E = 0 (b) E = 11ea98f3_0fb6_9423_99aa_9d94005c0b16_TB2997_11 11ea98f3_0fb6_9424_99aa_8fd4da579da3_TB2997_11 (c) E = 11ea98f3_0fb6_9425_99aa_59fc563783b7_TB2997_11 11ea98f3_0fb6_9426_99aa_150436140fc8_TB2997_11

At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?

Correct Answer
verified

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?

Correct Answer
verified

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) î. Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Correct Answer
verified

Correct Answer
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A

Correct Answer
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Exam 21: Gausss Law

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a +2.00-µC point charge placed at its center. Find the surface charge density (a) on the inner surface of the shell. (b) on the outer surface of the shell.

Correct Answerverified(a) -1590 ...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is

Correct AnswerverifiedShow Answer

Under electrostatic conditions, the electric field just outside the surface of any charged conductor

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A cone is resting on a tabletop as shown in the figure with its face horizontal. A uniform electric field of magnitude 4550 N/C points vertically upward. How much electric flux passes through the sloping side surface area of the cone?

Correct Answerverified6.36 N ∙ m2/C

Correct Answerverified(a) -5.00 µC (inner surface), ...View AnswerShow Answer

Correct AnswerverifiedShow Answer

A charge of 1.0 × 10-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answerverified(a) E = (b) At r =...View AnswerShow Answer

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

Correct AnswerverifiedShow Answer

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC. A point charge of +300 nC is present at the center. The surface charge density on the inner spherical surface is closest to

Correct AnswerverifiedShow Answer

The graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

Correct AnswerverifiedShow Answer

Correct Answerverified(a) E = 0 (b) E = 11ea98f3_0fb6_9423_99aa_9d94005c0b16_TB2997_11 11ea98f3_0fb6_9424_99aa_8fd4da579da3_TB2997_11 (c) E = 11ea98f3_0fb6_9425_99aa_59fc563783b7_TB2997_11 11ea98f3_0fb6_9426_99aa_150436140fc8_TB2997_11

At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?

Correct AnswerverifiedShow Answer

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?

Correct AnswerverifiedShow Answer

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) î. Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedA

Correct AnswerverifiedShow Answer

Correct Answer
verified
(a) -1590 ...
View Answer

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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6.36 N ∙ m²/C

Correct Answer
verified
(a) -5.00 µC (inner surface), ...
View Answer

Correct Answer
verified

A charge of 1.0 × 10^-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Correct Answer
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Correct Answer
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Correct Answer
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(a) E =
(b) At r =...
View Answer

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
verified
(a) E = 0 (b) E = 11ea98f3_0fb6_9423_99aa_9d94005c0b16_TB2997_11 11ea98f3_0fb6_9424_99aa_8fd4da579da3_TB2997_11 (c) E = 11ea98f3_0fb6_9425_99aa_59fc563783b7_TB2997_11 11ea98f3_0fb6_9426_99aa_150436140fc8_TB2997_11

Correct Answer
verified

Correct Answer
verified

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) î. Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Correct Answer
verified

Correct Answer
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A

Correct Answer
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