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A small charged plastic ball is vertically above another charged small ball in a frictionless test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the equilibrium distance between the balls in the test tube would become  A small charged plastic ball is vertically above another charged small ball in a frictionless test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the equilibrium distance between the balls in the test tube would become   A)   \sqrt { 2 }  d. B) 2d. C) 4d. D) 8d. E) d/4.


A) 2\sqrt { 2 } d.
B) 2d.
C) 4d.
D) 8d.
E) d/4.

F) A) and B)
G) B) and E)

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A negatively-charged rod is brought close to (but does not touch) two neutral spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres?


A) The sphere near the charged rod becomes positive and the other one becomes negative.
B) The sphere near the charged rod becomes negative and the other one becomes positive.
C) The spheres do not get any charge.
D) Both spheres become negative.
E) Both spheres become positive.

F) A) and E)
G) A) and D)

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Two tiny particles having charges of +7.00 μC and -9.00 μC are placed along the y-axis. The +7.00-µC particle is at y = 0.00 cm, and the other particle is at y = 40.00 cm. Where must a third charged particle be placed along the y-axis so that it does not experience any net electric force due to the other two particles?


A) 0.200 m
B) 2.99 m
C) -0.187 m
D) -2.99 m
E) 0.187 m

F) A) and B)
G) None of the above

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One point charge +Q is placed at the center of a square, and a second point charge -Q is placed at the upper-left corner of the square. It is observed that an electrostatic force of magnitude 2.0 N acts on the positive charge at the center. Now a third charge -Q is placed at the lower-left corner of the square, as shown in the figure. What is the magnitude of the net force that acts on the center charge now? One point charge +Q is placed at the center of a square, and a second point charge -Q is placed at the upper-left corner of the square. It is observed that an electrostatic force of magnitude 2.0 N acts on the positive charge at the center. Now a third charge -Q is placed at the lower-left corner of the square, as shown in the figure. What is the magnitude of the net force that acts on the center charge now?   A) 0.0 N B) 2.8 N C) 4.0 N D) 5.3 N


A) 0.0 N
B) 2.8 N
C) 4.0 N
D) 5.3 N

E) C) and D)
F) A) and B)

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As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is Q = - 90 nC, and all the other quantities are accurate to two significant figures. What is the magnitude of the net electrical force on Q due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is Q = - 90 nC, and all the other quantities are accurate to two significant figures. What is the magnitude of the net electrical force on Q due to the other two charges? (k = 1/4πε<sub>0</sub> = 9.0 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>)    A) 3.8 × 10<sup>-2</sup> N B) 2.8 × 10<sup>-2</sup> N C) 5.3 × 10<sup>-2</sup> N D) 7.1 × 10<sup>-2</sup> N


A) 3.8 × 10-2 N
B) 2.8 × 10-2 N
C) 5.3 × 10-2 N
D) 7.1 × 10-2 N

E) None of the above
F) All of the above

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A small object with a 5.0-μC charge is accelerating horizontally on a friction-free surface at 0.0050 m/s2 due only to an electric field. If the object has a mass of 2.0 g, what is the magnitude of the electric field?


A) 2.0 N/C
B) 4.0 N/C
C) 0.0020 N/C
D) 0.0040 N/C
E) 1.0 N/C

F) B) and E)
G) C) and D)

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A small 0.050-kg insulating sphere carries a charge of -60 μC and is hanging by a vertical silk thread from a fixed point in the ceiling. An external uniform vertical electric field is now applied. If the applied electric field has a magnitude of 3000 N/C and is directed downward, what is the tension in the silk thread? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)


A) 0.19 N
B) 0.31 N
C) 0.41 N
D) 0.52 N
E) 0.71 N

F) B) and E)
G) A) and B)

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A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod


A) is repelled by the sphere.
B) is attracted to the sphere.
C) feels no force due to the sphere.

D) All of the above
E) A) and B)

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When 1.0-µC point charge is 15 m from a second point charge, the force each one experiences a force of 1.0 µN. What is the magnitude of the second charge? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)


A) 25 C
B) 1.0 C
C) 10 nC
D) 0.025 C
E) 25 nC

F) B) and C)
G) None of the above

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The figure shows electric field lines arising from two small charged particles P and Q. Consider the following two statements: (i) The charge on P is smaller than the charge on Q. (ii) The electrostatic force on P is smaller than the force on Q. Which of the above statements are true? The figure shows electric field lines arising from two small charged particles P and Q. Consider the following two statements: (i) The charge on P is smaller than the charge on Q. (ii) The electrostatic force on P is smaller than the force on Q. Which of the above statements are true?   A) Only (i) is true. B) Only (ii) is true. C) Both (i) and (ii) are true. D) Neither (i) nor (ii) is true.


A) Only (i) is true.
B) Only (ii) is true.
C) Both (i) and (ii) are true.
D) Neither (i) nor (ii) is true.

E) B) and C)
F) A) and D)

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An electron is projected with an initial velocity v0 = 8.4 × 10710 ^ { 7 } m/s along the y-axis, which is the centerline between a pair of charged plates, as shown in the figure. The plates are 1.0 m long and are separated by 0.10 m. A uniform electric field of magnitude E in the +x-direction is present between the plates. If the magnitude of the acceleration of the electron is measured to be 8.9×1015 m/s28.9 \times 10 ^ { 15 } \mathrm {~m} / \mathrm { s } ^ { 2 } what is the magnitude of the electric field between the plates? (e = 1.6 × 10-19 C, melectron = 9.11 × 10-31 kg)  An electron is projected with an initial velocity v<sub>0</sub> = 8.4 ×  10 ^ { 7 }  m/s along the y-axis, which is the centerline between a pair of charged plates, as shown in the figure. The plates are 1.0 m long and are separated by 0.10 m. A uniform electric field of magnitude E in the +x-direction is present between the plates. If the magnitude of the acceleration of the electron is measured to be  8.9 \times 10 ^ { 15 } \mathrm {~m} / \mathrm { s } ^ { 2 }  what is the magnitude of the electric field between the plates? (e = 1.6 × 10<sup>-19</sup> C, m<sub>electron</sub> = 9.11 × 10<sup>-31</sup> kg)    A) 51,000 N/C B) 45,000 N/C C) 40,000 N/C D) 35,000 N/C E) 29,000 N/C


A) 51,000 N/C
B) 45,000 N/C
C) 40,000 N/C
D) 35,000 N/C
E) 29,000 N/C

F) None of the above
G) D) and E)

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The figure shows two tiny 5.0-g spheres suspended from very light 1.0-m-long threads. The spheres repel each other after each one is given the same positive charge and hang at rest when θ = 4.1°. What is the charge on each sphere? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) The figure shows two tiny 5.0-g spheres suspended from very light 1.0-m-long threads. The spheres repel each other after each one is given the same positive charge and hang at rest when θ = 4.1°. What is the charge on each sphere? (k = 1/4πε<sub>0</sub> = 9.0 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>)    A) 22 nC B) 89 nC C) 360 nC D) 180 nC E) 45 nC


A) 22 nC
B) 89 nC
C) 360 nC
D) 180 nC
E) 45 nC

F) B) and C)
G) A) and E)

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A +5.0-μC point charge is placed at the 0 cm mark of a meter stick and a -4.0-μC charge is placed at the 50 cm mark. What is the net electric field at the 30 cm mark? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)


A) 4.0 × 105 N/C
B) 5.0 × 105 N/C
C) 9.0 × 105 N/C
D) 1.4 × 106 N/C

E) B) and D)
F) None of the above

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An electron and a proton are released simultaneously from rest and start moving toward each other due to their electrostatic attraction, with no other forces present. Which of the following statements are true just before they are about to collide? (There could be more than one correct choice.)


A) They are closer to the to the initial position of the electron that to the initial position of the proton.
B) They are closer to the to the initial position of the proton that to the initial position of the electron.
C) They are at the midpoint of their initial separation.
D) They both have the same speed.
E) The electrostatic force on the proton is greater than the electrostatic force on the electron.

F) C) and D)
G) A) and C)

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An electron is placed in a uniform electric field of 4.5 × 104 N/C that points to the right. (e = 1.6 × 10-19 C, melectron = 9.11 × 10-31 kg) (a)What are the magnitude and direction of the force on the electron? (b)If the electron is released from rest, what is its speed after 3.0 ps?

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(a)7.2 × 1...

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Three equal positive point charges +q are placed at the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the center of the square? Three equal positive point charges +q are placed at the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the center of the square?   A) A B) B C) C D) D


A) A
B) B
C) C
D) D

E) B) and C)
F) B) and D)

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As shown in the figure, three charges are at the vertices of an equilateral triangle. The charge Q is 6.7 nC, and all the other quantities are accurate to two significant figures. What is the magnitude of the net electric force on the charge Q due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) As shown in the figure, three charges are at the vertices of an equilateral triangle. The charge Q is 6.7 nC, and all the other quantities are accurate to two significant figures. What is the magnitude of the net electric force on the charge Q due to the other two charges? (k = 1/4πε<sub>0</sub> = 9.0 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>)    A) 2.1 × 10<sup>-3</sup> N B) 1.2 × 10<sup>-3</sup> N C) 1.0 × 10<sup>-3</sup> N D) 1.4 × 10<sup>-3</sup> N


A) 2.1 × 10-3 N
B) 1.2 × 10-3 N
C) 1.0 × 10-3 N
D) 1.4 × 10-3 N

E) A) and C)
F) A) and B)

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(a) (a)    (b)    X and Y are two initially uncharged metal spheres on insulating stands, and they are in contact with each other. A positively charged rod R is brought close to X as shown in part (a) of the figure. Sphere Y is now moved away from X, as shown in part (b) . What are the final charge states of X and Y? A) Both X and Y are neutral. B) X is positive and Y is neutral. C) X is neutral and Y is positive. D) X is negative and Y is positive. E) Both X and Y are negative. (b) (a)    (b)    X and Y are two initially uncharged metal spheres on insulating stands, and they are in contact with each other. A positively charged rod R is brought close to X as shown in part (a) of the figure. Sphere Y is now moved away from X, as shown in part (b) . What are the final charge states of X and Y? A) Both X and Y are neutral. B) X is positive and Y is neutral. C) X is neutral and Y is positive. D) X is negative and Y is positive. E) Both X and Y are negative. X and Y are two initially uncharged metal spheres on insulating stands, and they are in contact with each other. A positively charged rod R is brought close to X as shown in part (a) of the figure. Sphere Y is now moved away from X, as shown in part (b) . What are the final charge states of X and Y?


A) Both X and Y are neutral.
B) X is positive and Y is neutral.
C) X is neutral and Y is positive.
D) X is negative and Y is positive.
E) Both X and Y are negative.

F) A) and D)
G) C) and D)

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Four point charges Q of equal magnitude and sign are arranged on three of the corners of the square of side d as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the upper right hand corner of the square? Four point charges Q of equal magnitude and sign are arranged on three of the corners of the square of side d as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the upper right hand corner of the square?   A) A B) B C) C D) D


A) A
B) B
C) C
D) D

E) A) and D)
F) All of the above

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A small glass bead has been charged to 1.9 nC. What is the strength of the electric field 2.0 cm from the center of the bead? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)


A) 4.3 × 104 N/C
B) 8.5 × 102 N/C
C) 8.1 × 10-5 N/C
D) 8.5 × 10-7 N/C

E) C) and D)
F) B) and C)

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