Charges and electric potential mastering physics

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HW3 Due: 11:59pm on Friday, October 5, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 23.10

Four electrons are located at the corners of a square 10.0 on a side, with an alpha particle at its midpoint.

Part A

How much work is done by the Coulomb force when the alpha particle moves to the midpoint of one of the sides of the square?

ANSWER:

Exercise 23.2

A point charge is held stationary at the origin. A second charge is placed at point , and the electric potential energy of the pair of charges is . When the second charge is moved to point , the electric force on the charge does

of work.

Part A

What is the electric potential energy of the pair of charges when the second charge is at point ?

Express your answer using two significant figures.

ANSWER:

Exercise 23.16

Two stationary point charges + 3.00 and + 2.00 are separated by a distance of 50.0 . An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges.

Part A

What is the speed of the electron when it is 10.0 from the + 3.00- charge?

ANSWER:

Exercise 23.39

nm

= W J

q1 q2 a

+5.4 × J10−8 b −1.9 × J10−8

b

J

nC nC cm

cm nC

= v m/s

11/30/2018 HW3

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The electric field at the surface of a charged, solid, copper sphere with radius 0.250 is 3500 , directed toward the center of the sphere. .

Part A

What is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere?

ANSWER:

Conceptual Question 23.01

Part A

If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.

ANSWER:

Conceptual Question 23.03

Part A

If the electrical potential in a region is constant, the electric field must be zero everywhere in that region.

ANSWER:

Conceptual Question 23.06

Part A

Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure. Which statement about the electric potential is true?

m N/C

= V V

True

False

True

False

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ANSWER:

Conceptual Question 23.08

Part A

Suppose you have two point charges of opposite sign. As you move them farther and farther apart, the potential energy of this system relative to infinity

ANSWER:

Conceptual Question 23.13

Part A

A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

Choose all that apply.

ANSWER:

The potential at points and are equal, and the potential at point is higher than the potential at point .A B C A

The potential at all three locations ( , , ) is the same because the field is uniform.A B C

The potential at point is the highest, the potential at point is the second highest, and the potential at point is the lowest.

A B C

The potential at points and are equal, and the potential at point is lower than the potential at point .A B C A

stays the same.

increases.

decreases.

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Prelecture Concept Question 23.01

Part A

A positive charge moves in the direction of an electric field. Which of the following statements are true?

Check all that apply.

ANSWER:

Prelecture Concept Question 23.03

Part A

A positive charge is moved from point A to point B along an equipotential surface. How much work is performed or required in moving the charge?

ANSWER:

The potential at the surface is higher then the potential at the center.

The potential at the center of the sphere is zero.

The potential at the center of the sphere is the same as the potential at the surface.

The potential at the center is the same as the potential at infinity.

The potential is highest at the center of the sphere.

The potential energy associated with the charge decreases.

The electric field does positive work on the charge.

The potential energy associated with the charge increases.

The electric field does negative work on the charge.

The electric field does not do any work on the charge.

The amount of work done on the charge cannot be determined without additional information.

Work is both performed and required in moving the charge from point A to point B.

Work is required in moving the positive charge from point A to point B.

No work is performed or required in moving the positive charge from point A to point B.

Work is performed in moving the positive charge from point A to point B.

11/30/2018 HW3

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Prelecture Concept Question 23.06

Part A

Which of the following statements are true?

Check all that apply.

ANSWER:

Problem 23.06

Part A

A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference, A - B, between points and ? ( = 1/4π = 8.99 × 109 N · m2/C2)

ANSWER:

An equipotential surface is a three-dimensional surface on which the electric potential is the same at every point.

Electric field lines and equipotential surfaces are always mutually perpendicular.

The potential energy of a test charge decreases as it moves along an equipotential surface.

When all charges are at rest, the surface of a conductor is always an equipotential surface.

The potential energy of a test charge increases as it moves along an equipotential surface.

V

V A B k ε0

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Problem 23.28

Part A

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. What is the maximum electric field magnitude between the cylinders? ( = 1/4π = 8.99 × 109 N · m2/C2)

ANSWER:

Problem 23.37

Part A

In a certain region, the electric potential due to a charge distribution is given by the equation where x and y are measured in meters and is in volts. At which point is the electric field equal to zero?

ANSWER:

96 kV

48 kV

0.00 V

48 V

96 V

k ε0

10,000 V/m

18,000 V/m

22,000 V/m

26,000 V/m

14,000 V/m

V (x, y) = 2xy − − y,x2

V

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Problem 24.66

A parallel-plate capacitor is made from two plates 12.0 on each side and 4.50 apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas of dielectric constant 3.40. (See the figure below.) An 18.0 battery is connected across the plates.

Part A

What is the capacitance of this combination?

ANSWER:

Part B

How much energy is stored in the capacitor?

ANSWER:

Part C

If we remove the Plexiglas, but change nothing else, how much energy will be stored in the capacitor?

ANSWER:

Problem 24.57

= 0.5 m, = 0.5 mx y

= 1 m, = 1 mx y

= 1 m, = 0.5 mx y

= 0.5 m, = 1 mx y

= 0 m, = 0 mx y

cm mm V

= C F

= U J

= U J

11/30/2018 HW3

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Three capacitors having capacitances of 9.0 , 8.0 , and 4.7 are connected in series across a 30- potential difference.

Part A

What is the charge on the 4.7 capacitor?

Express your answer using two significant figures.

ANSWER:

Part B

What is the total energy stored in all three capacitors?

Express your answer using two significant figures.

ANSWER:

Part C

The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?

Express your answer using two significant figures.

ANSWER:

Part D

What is the total energy now stored in the capacitors?

Express your answer using two significant figures.

ANSWER:

Problem 24.59

In the figure , each capacitance is 7.2 , and each capacitance is 4.8 .

μF μF μF V

μF

= Q3 C

= U J

= V V

= U J

C1 μF C2 μF

11/30/2018 HW3

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Part A

Compute the equivalent capacitance of the network between points a and b.

Express your answer using two significant figures.

ANSWER:

Part B

Compute the charge on the capacitor nearest to a when = 420 .

Express your answer using two significant figures.

ANSWER:

Part C

Compute the charge on the capacitor nearest to b when = 420 .

ANSWER:

Part D

Compute the charge on the capacitor nearest to a and b when = 420 .

Express your answer using two significant figures.

ANSWER:

= Ceq F

C1 Vab V

= Qa1 C

C1 Vab V

= Qb1 C

C2 Vab V

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Part E

With 420 across a and b, compute .

Express your answer using two significant figures.

ANSWER:

Problem 24.51

For the capacitor network shown in the Figure , the potential difference across is 12.0 .

Part A

Find the total energy stored in this network.

ANSWER:

Part B

Find the energy stored in the 4.80- capacitor.

ANSWER:

Problem 24.35

= Q2 C

V Vcd

= Vcd V

ab V

= U μJ

μF

= U4.80 μF μJ

11/30/2018 HW3

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Part A

A parallel-plate capacitor consists of two parallel, square plates that have dimensions 1.0 cm by 1.0 cm. If the plates are separated by 5 mm, and the space between them is filled with teflon, what is the capacitance of this capacitor? (The dielectric constant for teflon is 2.1, and ε0 = 8.85 × 10-12 C2/N · m2.)

ANSWER:

Problem 24.32

Part A

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. What is the voltage now across the capacitor?

ANSWER:

Problem 24.29

Part A

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m2, and the separation of the plates is 0.080 mm. An electric field of 5.3 × 106 V/m is present between the plates. What is the energy density between the plates? ( = 8.85 × 10-12 C2/N · m2)

ANSWER:

0.37 pF

0.42 pF

0.18 pF

8.9×10−2 pF

5.0 V

80 V

20 V

2.5 V

10 V

ε0

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Problem 24.24

Part A

A 8.00-μF parallel-plate capacitor has charges of 60.0 μC on its plates. How much potential energy is stored in this capacitor?

ANSWER:

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210 J/m3

170 J/m3

84 J/m3

250 J/m3

124 J/m3

205 μJ

225 μJ

215 μJ

195 μJ

235 μJ