Deck 16: Electric Charge and Electric Field

Question 1

Write the word or phrase that best completes each statement or answers the question.
Two small identically charged balls are a certain distance apart. The vectors in the figure show the magnitude and direction of the electrostatic force on each ball due to the other one. Suppose that the charge on the left ball is now doubled (represented by two plus signs). Which vector diagram below best represents the forces that now act on each of the two balls?

A)

B)

C)

D)

Answer 1

C

Question 2

Write the word or phrase that best completes each statement or answers the question.
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) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $D$

Answer 2

D

Question 3

Write the word or phrase that best completes each statement or answers the question.
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) $2 d$ .
B) $\sqrt { 2 } d$ .
C) $d / 4$ .
D) $8 d$ .
E) $4 d$ .

Answer 3

A

Question 4

Write the word or phrase that best completes each statement or answers the question.
A hydrogen nucleus, which has a charge $+ e$ , is situated to the left of a carbon nucleus, which has a charge $+ 6 \mathrm { e }$ . Which statement is true?

A) The electrical force experienced by the hydrogen nucleus is to the right, and the magnitude is equal to the force exerted on the carbon nucleus.
B) The electrical force experienced by the hydrogen nucleus is to the left, and the magnitude is equal to the force exerted on the carbon nucleus.
C) The electrical force experienced by the hydrogen nucleus is to the left, and the magnitude is less than the force exerted on the carbon nucleus.
D) The electrical force experienced by the hydrogen nucleus is to the left, and the magnitude is greater than the force exerted on the carbon nucleus.

Question 5

Choose the one alternative that best completes the statement or answers the question.
An electron is initially moving to the right when it enters a uniform electric field directed upwards, as shown in the figure. Which trajectory $( \mathbf { X } , \mathbf { Y } , \mathbf { Z }$ , or $\mathbf { W } )$ will the electron follow in the field?

A) trajectory W
B) trajectory $\mathbf { X }$
C) trajectory Y
D) trajectory $Z$

Question 6

Write the word or phrase that best completes each statement or answers the question.
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) Both spheres become positive.
D) The spheres do not get any charge.
E) Both spheres become negative.

Question 7

Write the word or phrase that best completes each statement or answers the question.
Two very small plastic balls of equal mass are released from rest. One of them carries $+ 10 \mu \mathrm { C }$ of excess charge and the other one carries $+ 1 \mu \mathrm { C }$ of charge. No other charges or fields are present. Which of the following statements are true about them as they move away from each other? (There may be more than one correct choice.)

A) The acceleration of the $10 - \mu \mathrm { C }$ ball is 10 times that of the $1 - \mu \mathrm { C }$ ball.
B) The acceleration of the balls keeps increasing.
C) The acceleration of the $1 - \mu \mathrm { C }$ ball is 10 times that of the $10 - \mu \mathrm { C }$ ball.
D) The balls always have accelerations of equal magnitude.
E) The speed of the balls keeps increasing.

Question 8

Write the word or phrase that best completes each statement or answers the question.
$X$ 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) $X$ is neutral and $Y$ is positive.
B) $X$ is positive and $Y$ is neutral.
C) Both $X$ and $Y$ are negative.
D) $X$ is negative and $Y$ is positive.
E) Both $X$ and $Y$ are neutral.

Question 9

Write the word or phrase that best completes each statement or answers the question.
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 both have the same speed.
B) The electrostatic force on the proton is greater than the electrostatic force on the electron.
C) They are closer to the to the initial position of the electron that to the initial position of the proton.
D) They are closer to the to the initial position of the proton that to the initial position of the electron.
E) They are at the midpoint of their initial separation.

Question 10

Write the word or phrase that best completes each statement or answers the question.
Two equal and opposite charges are a small distance apart, forming an electric dipole. A positive charge $+ q$ is placed above these charges, as shown in the figure, equidistant from both of them. Which diagram below best gives the direction of the net force the dipole exerts on the charge $+ q$ ?
$+ q$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude $F$ due to the other. With time, charge gradually diminishes on both spheres by leaking off. When each of the spheres has lost half its initial charge, what will be the magnitude of the electrostatic force on each one?

A) $1 / 4 F$
B) $1 / \sqrt { 2 } F$
C) $1 / 16 \mathrm {~F}$
D) $1 / 8 \mathrm {~F}$
E) $1 / 2 \mathrm {~F}$

Question 12

Write the word or phrase that best completes each statement or answers the question.
Two uncharged metal spheres, #1 and #2, are mounted on insulating support rods. A third metal sphere, carrying a positive charge, is then placed near #2. Now a copper wire is momentarily connected between $\# 1$ and #2 and then removed. Finally, sphere $\# 3$ is removed. In this final state

A) sphere #1 carries positive charge and #2 carries negative charge.
B) spheres #1 and #2 are still uncharged.
C) sphere #1 carries negative charge and #2 carries positive charge.
D) spheres #1 and #2 both carry negative charge.
E) spheres #1 and #2 both carry positive charge.

Question 13

Write the word or phrase that best completes each statement or answers the question.
Four point charges of equal magnitudes but with varying signs are arranged on three of the corners and at the center of the square of side $d$ as shown in the figure. Which one of the arrows shown represents the net force acting on the center charge?

A) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $D$

Question 14

Write the word or phrase that best completes each statement or answers the question.
Two tiny beads are $25 \mathrm {~cm}$ apart with no other charges or fields present. Bead A carries $10 \mu \mathrm { C }$ of charge and bead B carries $1 \mu \mathrm { C }$ . Which one of the following statements is true about the magnitudes of the electric forces on these beads?

A) The force on $A$ is exactly equal to the force on B.
B) The force on $B$ is 100 times the force on $A$ .
C) The force on $B$ is 10 times the force on $A$ .
D) The force on $A$ is 10 times the force on $B$ .
E) The force on $A$ is 100 times the force on $B$ .

Question 15

Write the word or phrase that best completes each statement or answers the question.
Two point charges, $Q _ { 1 }$ and $Q _ { 2 }$ , are separated by a distance $R$ . If the magnitudes of both charges are halved and their separation is also halved, what happens to the electrical force that each charge exerts on the other one?

A) It increases by a factor of 4 .
B) It increases by a factor of 8 .
C) It remains the same.
D) It increases by a factor of 16 .
E) It increases by a factor of 2 .

Question 16

Write the word or phrase that best completes each statement or answers the question.
Three equal charges $+ Q$ are at three of the corners of a square of side $d$ . A fourth charge $+ Q$ of equal magnitude is at the center of the square as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the center of the square?

A) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $\mathrm { D }$

Question 17

Write the word or phrase that best completes each statement or answers the question.
In outer space, a positive charge $q$ is released near a positive fixed charge $Q$ , as shown in the figure. As $q$ moves away from $Q$ , what is true about the motion of $q$ ? (There may be more than one correct choice.)

A) It will move with increasing speed.
B) It will move with decreasing speed.
C) It will move with decreasing acceleration.
D) It will move with increasing acceleration.
E) It will move with constant acceleration.

Question 18

Write the word or phrase that best completes each statement or answers the question.
Two point charges, $Q _ { 1 }$ and $Q _ { 2 }$ , are separated by a distance $R$ . If the magnitudes of both charges are doubled and their separation is also doubled, what happens to the electrical force that each charge exerts on the other one?

A) It increases by a factor of $\sqrt { 2 }$ .
B) It remains the same.
C) It increases by a factor of 2 .
D) It is reduced by a factor of $\sqrt { 2 }$ .
E) It increases by a factor of 4 .

Question 19

Write the word or phrase that best completes each statement or answers the question.
Four point charges of varying magnitude and sign are arranged on 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 point charge with a charge $+ Q$ ?

A) $A$
B) $\mathrm { B }$
C) $\mathrm { C }$
D) D

Question 20

Write the word or phrase that best completes each statement or answers the question.
Four point charges of equal magnitude but with varying signs are arranged on three of the corners and at the center of the square of side $d$ as shown in the figure. Which one of the arrows shown represents the net force acting on the center charge?

A) $\mathrm { A }$
B) $B$
C) $C$
D) D

Question 21

Choose the one alternative that best completes the statement or answers the question.
The figure shows electric field lines arising from two small charged particles $P$ and $Q$ . Consider the following two statements:
(i) The charge on $\mathrm { P }$ is smaller than the charge on $\mathrm { Q }$ .
(ii) The electrostatic force on $\mathrm { P }$ 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.

Question 22

Choose the one alternative that best completes the statement or answers the question.
A piece of plastic has a net charge of $+ 2.00 \mu \mathrm { C }$ . How many more protons than electrons does this piece of plastic have? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $1.25 \times 10 ^ { 13 }$
B) $2.50 \times 10 ^ { 13 }$
C) $3.01 \times 10 ^ { 23 }$
D) $2.50 \times 10 ^ { 19 }$
E) $1.25 \times 10 ^ { 19 }$

Question 23

Choose the one alternative that best completes the statement or answers the question.
Which one of the arrows shown in the figure best represents the direction of the electric field between the two uniformly charged metal plates?

A) $\mathrm { A }$
B) $B$
C) $C$
D) $D$
E) None of the above

Question 24

Choose the one alternative that best completes the statement or answers the question.
What is the charge on $1.0 \mathrm {~kg}$ of protons? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A) $9.6 \times 10 ^ { 7 } \mathrm { C }$
B) $1000 \mathrm { C }$
C) $1.0 \mathrm { C }$
D) $6.0 \times 10 ^ { 26 } \mathrm { C }$
E) $6.0 \times 10 ^ { 23 } \mathrm { C }$

Question 25

Choose the one alternative that best completes the statement or answers the question.
The figure shows two unequal charges, $+ q$ and $- Q$ . Charge $- Q$ has greater magnitude than charge $+ q$ . Point $\mathrm { X }$ is midway between the charges. In what section of the line will there be a point where the resultant electric field is zero?

A) VW
B) $W X$
C) $X Y$
D) $Y Z$

Question 26

Choose the one alternative that best completes the statement or answers the question.
The electric field at point $P$ due to a point charge $Q$ a distance $R$ away from $P$ has magnitude $E$ . In order to double the magnitude of the field at $P$ , you could

A) double the distance to $2 R$ .
B) double the charge to $2 Q$ and at the same time reduce the distance to $R / 2$ .
C) reduce the distance to $R / 4$ .
D) double the charge to $2 Q$ .
E) reduce the distance to $R / 2$ .

Question 27

Choose the one alternative that best completes the statement or answers the question.
An asteroid of mass $58,000 \mathrm {~kg}$ carrying a negative charge of $15 \mu \mathrm { C }$ is $180 \mathrm {~m}$ from a second asteroid of mass $52,000 \mathrm {~kg}$ carrying a negative charge of $11 \mu \mathrm { C }$ . What is the magnitude of the net force the asteroids exert upon each other, assuming we can treat them as point particles? $\left( G = 6.67 \times 10 ^ { - 11 } \right.$ $\mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $570,000 \mathrm {~N}$
B) $0.000040 \mathrm {~N}$
C) $0.0062 \mathrm {~N}$
D) $510,000 \mathrm {~N}$

Question 28

Write the word or phrase that best completes each statement or answers the question.
The figure shows four Gaussian surfaces surrounding a distribution of charges.
(a) Which Gaussian surfaces have an electric flux of $+ q / \varepsilon _ { 0 }$ through them?
(b) Which Gaussian surfaces have no electric flux through them?

Question 29

Choose the one alternative that best completes the statement or answers the question.
If a charge generator builds a negative static charge of $- 7.00 \mu \mathrm { C }$ , how many electrons are transferred to it during this process. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $4.38 \times 10 ^ { 13 }$
B) $43.8$
C) $7.0$
D) $1.12 \times 10 ^ { - 18 }$

Question 30

Choose the one alternative that best completes the statement or answers the question.
Three equal negative point charges $- q$ are placed at three of 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 vacant corner of the square?

A) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $\mathrm { D }$

Question 31

Choose the one alternative that best completes the statement or answers the question.
Two stationary point charges $q _ { 1 }$ and $q _ { 2 }$ are shown in the figure along with a sketch of some field lines representing the electric field produced by them. What can you deduce from the sketch?

A) $q _ { 1 }$ is negative and $q _ { 2 }$ is positive; the magnitudes are equal.
B) $q _ { 1 }$ and $q _ { 2 }$ have the same sign; the magnitude of $q _ { 1 }$ is greater than the magnitude of $q _ { 2 }$ .
C) $q 1$ is negative and $q _ { 2 }$ is positive; the magnitude of $q _ { 1 }$ is less than the magnitude of $q _ { 2 }$ .
D) $q _ { 1 }$ and $q _ { 2 }$ have the same sign; the magnitudes are equal.
E) $q _ { 1 }$ is positive and $q _ { 2 }$ is negative; the magnitude of $q _ { 1 }$ is greater than the magnitude of $q _ { 2 }$ .

Question 32

Choose the one alternative that best completes the statement or answers the question.
Two electrons are $20.0 \mathrm {~mm}$ apart at closest approach. What is the magnitude of the maximum electric force that they exert on each other? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , k = 1 / 4 \pi \varepsilon _ { 0 } = 9.010 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $5.8 \times 10 ^ { - 27 } \mathrm {~N}$
B) $2.3 \mathrm {~N}$
C) $2.3 \times 10 ^ { 10 } \mathrm {~N}$
D) $5.8 \times 10 ^ { - 25 } \mathrm {~N}$

Question 33

Choose the one alternative that best completes the statement or answers the question.
The force of attraction that a $- 40.0 \mu \mathrm { C }$ point charge exerts on $\mathrm { a } + 108 \mu \mathrm { C }$ point charge has magnitude $4.00 \mathrm {~N}$ . How far apart are these two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $2.10 \mathrm {~m}$
B) $3.12 \mathrm {~m}$
C) $2.49 \mathrm {~m}$
D) $3.67 \mathrm {~m}$
E) $1.13 \mathrm {~m}$

Question 34

Choose the one alternative that best completes the statement or answers the question.
Four tiny charged particles (two having a charge $+ Q$ and two having a charge $- Q$ ) are distributed on the $x$ - and $y$ -axes as shown in the figure. Each charge is equidistant from the origin. In which direction is the net electric field at the point $P$ on the $y$ -axis?

A) upwards and towards the left
B) directly left ( $- x$ direction)
C) upwards and towards the right
D) directly up (in the $+ y$ direction)
E) The net field is zero, so there is no direction.

Question 35

Choose the one alternative that best completes the statement or answers the question.
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) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $\mathrm { D }$

Question 36

Choose the one alternative that best completes the statement or answers the question.
How many electrons are necessary to produce $1.0 \mathrm { C }$ of negative charge? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $1.6 \times 10 ^ { 9 }$
B) $1.6 \times 10 ^ { 19 }$
C) $6.3 \times 10 ^ { 9 }$
D) $6.3 \times 10 ^ { 18 }$
E) $6.0 \times 10^{23}$

Question 37

Choose the one alternative that best completes the statement or answers the question.
Gaussian surfaces $A$ and B enclose the same positive charge $+ Q$ . The area of Gaussian surface A is three times larger than that of Gaussian surface B. The electric flux through Gaussian surface $A$ is

A) equal to the flux of electric field through Gaussian surface B.
B) three times smaller than the flux of electric field through Gaussian surface B.
C) unrelated to the flux of electric field through Gaussian surface B.
D) nine times larger than the flux of electric field through Gaussian surface B.
E) three times larger than the flux of electric field through Gaussian surface B.

Question 38

Choose the one alternative that best completes the statement or answers the question.
Three equal negative point charges $- q$ are placed at three of 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) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $D$

Question 39

Choose the one alternative that best completes the statement or answers the question.
Three equal-magnitude point charges of varying signs 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) $\mathrm { A }$
B) $B$
C) $\mathrm { C }$
D) $\mathrm { D }$

Question 40

Choose the one alternative that best completes the statement or answers the question.
Three equal-magnitude point charges of varying signs are placed at three of 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 vacant corner of the square?

A) $A$
B) $B$
C) $\mathrm { C }$
D) $\mathrm { D }$

Question 41

Choose the one alternative that best completes the statement or answers the question.
Three point charges are located on the $x$ -axis at the following positions: $Q _ { 1 } = + 2.00 \mu \mathrm { C }$ is at $x =$ $1.00 \mathrm {~m} , Q _ { 2 } = + 3.00 \mu \mathrm { C }$ is at $\mathrm { x } = 0.00$ , and $Q _ { 3 } = - 5.00 \mu \mathrm { C }$ is at $x = - 1.00 \mathrm {~m}$ . What is the magnitude of the electric force on $Q 2 ? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right.$ )

A) $0.135 \mathrm {~N}$
B) $0.0810 \mathrm {~N}$
C) $0.0540 \mathrm {~N}$
D) $0.189 \mathrm {~N}$
E) $0.158 \mathrm {~N}$

Question 42

Choose the one alternative that best completes the statement or answers the question.
Two $10 \phi$ coins (dimes) carrying identical charges are lying $2.5 \mathrm {~m}$ apart on a table. If each of these coins experiences an electrostatic force of magnitude $2.0 \mathrm {~N}$ due to the other coin, how large is the charge on each coin? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $26 \mu \mathrm { C }$
B) $2.6 \mu \mathrm { C }$
C) $6.7 \mu \mathrm { C }$
D) $5.2 \mu \mathrm { C }$
E) $52 \mu \mathrm { C }$

Question 43

Choose the one alternative that best completes the statement or answers the question.
The zirconium nucleus contains 40 protons, and an electron is $1.0 \mathrm {~nm}$ from the nucleus. What is the electric force on the electron due to the nucleus? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $\mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $1000 \mathrm { C }$
B) $3.7 \mathrm { nN }$
C) $9.2 \mathrm { nN }$
D) $6.8 \mathrm { nN }$
E) $2.9 \mathrm { nN }$

Question 44

Choose the one alternative that best completes the statement or answers the question.
A proton is located at the point $( x = 1.0 \mathrm {~nm} , y = 0.0 \mathrm {~nm} )$ and an electron is located at the point $( x = 0.0 \mathrm {~nm} , y = 4.0 \mathrm {~nm} )$ . Find the magnitude of the electrostatic force that each one exerts on the other. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $5.9 \times 10 ^ { - 15 } \mathrm {~N}$
B) $5.3 \times 10 ^ { 8 } \mathrm {~N}$
C) $1.4 \times 10 ^ { - 11 } \mathrm {~N}$
D) $5.3 \times 10 ^ { - 18 } \mathrm {~N}$

Question 45

Choose the one alternative that best completes the statement or answers the question.
Two tiny particles having charges of $+ 5.00 \mu \mathrm { C }$ and $+ 7.00 \mu \mathrm { C }$ are placed along the $x$ -axis. The $+ 5.00 - \mu \mathrm { C }$ particle is at $x = 0.00 \mathrm {~cm}$ , and the other particle is at $x = 100.00 \mathrm {~cm}$ . Where on the $x$ -axis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles?

A) $45.8 \mathrm {~cm}$
B) $9.12 \mathrm {~cm}$
C) $4.58 \mathrm {~cm}$
D) $50 \mathrm {~cm}$
E) $91.2 \mathrm {~cm}$

Question 46

Choose the one alternative that best completes the statement or answers the question.
A particle of charge $+ 2 q$ is placed at the origin and particle of charge $- q$ is placed on the $x$ -axis at $x$ $= 2 \mathrm { a }$ . Where on the $x$ -axis can a third positive charge be placed so that the net electric force on it is zero?

A) $9.3 \mathrm { a }$
B) $8.6 a$
C) $1.0 a$
D) $3.4 a$
E) $6.8 a$

Question 47

Write the word or phrase that best completes each statement or answers the question.
A point charge $Q _ { 1 } = + 6.0 \mathrm { nC }$ is at the point $( 0.30 \mathrm {~m} , 0.00 \mathrm {~m} )$ ; a charge $Q _ { 2 } = - 1.0 \mathrm { nC }$ is at $( 0.00 \mathrm {~m} , 0.10 \mathrm {~m} )$ , and a charge $Q _ { 3 } = + 5.0 \mathrm { nC }$ is at $( 0.00 \mathrm {~m} , 0.00 \mathrm {~m} )$ . What are the magnitude and direction of the net force on the $+ 5.0 - \mathrm { nC }$ charge due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 48

Write the word or phrase that best completes each statement or answers the question.
Three point charges are placed on the $x$ -axis, as follows. A charge of $+ 2.0 \mu \mathrm { C }$ is at the origin, a charge of $- 2.0 \mu \mathrm { C }$ is at $x = 50 \mathrm {~cm}$ , and a charge of $+ 4.0 \mu \mathrm { C }$ is at $x = 100 \mathrm {~cm}$ . What are the magnitude and direction of the electrostatic force on the charge at the origin due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 49

Choose the one alternative that best completes the statement or answers the question.
When $1.0 - \mu \mathrm { C }$ point charge is $15 \mathrm {~m}$ from a second point charge, the force each one experiences a force of $1.0 \mu \mathrm { N }$ . What is the magnitude of the second charge? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $10 \mathrm { nC }$
B) $25 \mathrm { nC }$
C) $1.0 \mathrm { C }$
D) $0.025 \mathrm { C }$
E) $25 \mathrm { C }$

Question 50

Choose the one alternative that best completes the statement or answers the question.
Two equally charged tiny spheres of mass $1.0 \mathrm {~g}$ are placed $2.0 \mathrm {~cm}$ apart. When released, they begin to accelerate away from each other at $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$ . What is the magnitude of the charge on each sphere, assuming only that the electric force is present? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $140 \mathrm { nC }$
B) $95 \mathrm { nC }$
C) $120 \mathrm { nC }$
D) $75 \mathrm { nC }$

Question 51

Choose the one alternative that best completes the statement or answers the question.
Three identical $3.0 - \mu \mathrm { C }$ charges are placed at the vertices of an equilateral triangle that measures 30 $\mathrm { cm }$ on a side. What is the magnitude of the electrostatic force on any one of the charges? $( k = 1 / 4 \pi$ $\varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $1.8 \mathrm {~N}$
B) $2.0 \mathrm {~N}$
C) $2.2 \mathrm {~N}$
D) $2.4 \mathrm {~N}$
E) $1.6 \mathrm {~N}$

Question 52

Choose the one alternative that best completes the statement or answers the question.
Two point charges each experience a $1 - \mathrm { N }$ electrostatic force when they are $2 \mathrm {~cm}$ apart. If they are moved to a new separation of $8 \mathrm {~cm}$ , what is the magnitude of the electric force on each of them?

A) $1 / 16 \mathrm {~N}$
B) $1 / 8 \mathrm {~N}$
C) $2 \mathrm {~N}$
D) $1 / 2 \mathrm {~N}$
E) $1 / 4 \mathrm {~N}$

Question 53

Choose the one alternative that best completes the statement or answers the question.
The three point charges $+ 4.0 \mu \mathrm { C } , - 5.0 \mu \mathrm { C }$ , and $- 9.0 \mu \mathrm { C }$ are placed on the $x$ -axis at the points $x = 0$ $\mathrm { cm } , x = 40 \mathrm {~cm}$ , and $x = 120 \mathrm {~cm}$ , respectively. What is the $x$ component of the electrostatic force on the $- 9.0 \mu \mathrm { C }$ charge due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $0.64 \mathrm {~N}$
B) $- 0.55 \mathrm {~N}$
C) $- 0.41 \mathrm {~N}$
D) $0.55 \mathrm {~N}$
E) $0.41 \mathrm {~N}$

Question 54

Choose the one alternative that best completes the statement or answers the question.
Two tiny particles carrying like charges of the same magnitude are $1.0 \mathrm {~mm}$ apart. If the electric force on one of them is $5.0 \mathrm {~N}$ , what is the magnitude of the charge on each of these particles? $( k =$ $1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $2.4 \times 10 ^ { - 2 } \mathrm { C }$
B) $4.5 \times 10 ^ { 4 } \mathrm { C }$
C) $2.4 \times 10 ^ { - 8 } \mathrm { C }$
D) $2.4 \times 10 ^ { - 5 } \mathrm { C }$

Question 55

Write the word or phrase that best completes each statement or answers the question.
Consider a container of $2.0 \mathrm {~g}$ of hydrogen, $\mathrm { H } 2$ (one mole). Suppose you removed all the electrons and moved them to the other side of the earth (Earth's radius is $6380 \mathrm {~km} , k = 1 / 4$ $\pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , \mathrm {~N} _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 }$ molecules $\left. / \mathrm { mol } , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$
(a) How much charge is left behind after you remove the electrons?
(b) What electric force do the protons exert on the electrons after they are separated as described?

Question 56

Choose the one alternative that best completes the statement or answers the question.
Two tiny particles having charges of $+ 7.00 \mu \mathrm { C }$ and $- 9.00 \mu \mathrm { C }$ are placed along the $y$ -axis. The $+ 7.00 - \mu \mathrm { C }$ particle is at $y = 0.00 \mathrm {~cm}$ , and the other particle is at $y = 40.00 \mathrm {~cm}$ . 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) $2.99 \mathrm {~m}$
B) $- 2.99 \mathrm {~m}$
C) $0.187 \mathrm {~m}$
D) $0.200 \mathrm {~m}$
E) $- 0.187 \mathrm {~m}$

Question 57

Choose the one alternative that best completes the statement or answers the question.
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 $2.0 \mathrm {~N}$ 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) $4.0 \mathrm {~N}$
B) $0.0 \mathrm {~N}$
C) $5.3 \mathrm {~N}$
D) $2.8 \mathrm {~N}$

Question 58

Write the word or phrase that best completes each statement or answers the question.
How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right.$ , $m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

Question 59

Choose the one alternative that best completes the statement or answers the question.
Two tiny beads, each of mass $3.2 \mathrm {~g}$ , carry equal-magnitude charges. When they are placed $6.4 \mathrm {~cm}$ apart and released in outer space, they begin to accelerate toward each other at $538 \mathrm {~m} / \mathrm { s } ^ { 2 }$ . What is the magnitude of the charge on each bead? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right.$ )

A) $1800 \mathrm { nC }$
B) $890 \mathrm { nC }$
C) $44 \mathrm { nC }$
D) $1300 \mathrm { nC }$
E) $510 \mathrm { nC }$

Question 60

Choose the one alternative that best completes the statement or answers the question.
Suppose you wanted to hold up an electron against the force of gravity by the attraction of a fixed proton some distance above it. How far above the electron would the proton have to be? $( k = 1 / 4 \pi$ $\left. \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

A) $3.7 \mathrm {~m}$
B) $5.1 \mathrm {~m}$
C) $1.5 \mathrm {~m}$
D) $4.6 \mathrm {~m}$
E) $2.3 \mathrm {~m}$

Question 61

Choose the one alternative that best completes the statement or answers the question.
A proton is placed in an electric field of intensity $800 \mathrm {~N} / \mathrm { C }$ . What are the magnitude and direction of the acceleration of the proton due to this field? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , \mathrm { m } _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A) $76.6 \times 10 ^ { 10 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ opposite to the electric field
B) $7.66 \times 10 ^ { 10 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ opposite to the electric field
C) $7.66 \times 10 ^ { 10 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ in the direction of the electric field
D) $7.66 \times 10 ^ { 9 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ opposite to the electric field
E) $76.6 \times 10^{10} \mathrm {~m} / \mathrm { s } ^ { 2 }$ in the direction of the electric field

Question 62

Write the word or phrase that best completes each statement or answers the question.
An electron is placed in a uniform electric field of $4.5 \times 104 \mathrm {~N} / \mathrm { C }$ that points to the right. $( e =$ $1.6 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 - 31 \mathrm {~kg}$ )
(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 $3.0 \mathrm { ps }$ ?

Question 63

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, three charges are at the vertices of an equilateral triangle. The charge $Q$ is $6.7 \mathrm { nC }$ , 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? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $m ^ { 2 } / C ^ { 2 }$ )

A) $1.4 \times 10 ^ { - 3 } \mathrm {~N}$
B) $1.0 \times 10 ^ { - 3 } \mathrm {~N}$
C) $2.1 \times 10 ^ { - 3 } \mathrm {~N}$
D) $1.2 \times 10 ^ { - 3 } \mathrm {~N}$

Question 64

Choose the one alternative that best completes the statement or answers the question.
A particle with a charge of $+ 4.0 \mu \mathrm { C }$ has a mass of $5.0 \mathrm {~g}$ . What magnitude electric field directed upward will exactly balance the weight of the particle?

A) $4.4 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { C }$
B) $5.1 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { C }$
C) $1.2 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { C }$
D) $4.1 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { C }$
E) $8.2 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { C }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
A small $0.050 - \mathrm { kg }$ insulating sphere carries a charge of $- 60 \mu \mathrm { C }$ 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 $3000 \mathrm {~N} / \mathrm { C }$ and is directed downward, what is the tension in the silk thread? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $0.19 \mathrm {~N}$
B) $0.31 \mathrm {~N}$
C) $0.71 \mathrm {~N}$
D) $0.41 \mathrm {~N}$
E) $0.52 \mathrm {~N}$

Question 66

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is $Q = - 90 \mathrm { nC }$ , 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? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \right.$ $\mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $7.1 \times 10 ^ { - 2 } \mathrm {~N}$
B) $5.3 \times 10 ^ { - 2 } \mathrm {~N}$
C) $2.8 \times 10 ^ { - 2 } \mathrm {~N}$
D) $3.8 \times 10 ^ { - 2 } \mathrm {~N}$

Question 67

Choose the one alternative that best completes the statement or answers the question.
A small glass bead has been charged to $1.9 \mathrm { nC }$ . What is the strength of the electric field $2.0 \mathrm {~cm}$ from the center of the bead? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $8.1 \times 10 ^ { - 5 } \mathrm {~N} / \mathrm { C }$
B) $8.5 \times 10 ^ { 2 } \mathrm {~N} / \mathrm { C }$
C) $4.3 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { C }$
D) $8.5 \times 10 ^ { - 7 } \mathrm {~N} / \mathrm { C }$

Question 68

Choose the one alternative that best completes the statement or answers the question.
A small object with a $5.0 - \mu \mathrm { C }$ charge is accelerating horizontally on a friction-free surface at $0.0050$ $\mathrm { m } / \mathrm { s } 2$ due only to an electric field. If the object has a mass of $2.0 \mathrm {~g}$ , what is the magnitude of the electric field?

A) $1.0 \mathrm {~N} / \mathrm { C }$
B) $0.0020 \mathrm {~N} / \mathrm { C }$
C) $4.0 \mathrm {~N} / \mathrm { C }$
D) $2.0 \mathrm {~N} / \mathrm { C }$
E) $0.0040 \mathrm {~N} / \mathrm { C }$

Question 69

Choose the one alternative that best completes the statement or answers the question.
A pair of charged conducting plates produces a uniform field of $12,000 \mathrm {~N} / \mathrm { C }$ , directed to the right, between the plates. The separation of the plates is $40 \mathrm {~mm}$ . An electron is projected from plate $A$ , directly toward plate $\mathrm { B }$ , with an initial speed of $v _ { 0 } = 2.0 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ . What is the speed of the electron as it strikes plate $B$ ? $\left( e = 1.6 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

A) $2.1 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
B) $1.5 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
C) $1.2 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
D) $2.4 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
E) $1.8 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$

Question 70

Choose the one alternative that best completes the statement or answers the question.
The figure shows two tiny $5.0 - \mathrm { g }$ 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 $\theta$ $= 4.1 ^ { \circ }$ . What is the charge on each sphere $? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $360 \mathrm { nC }$
B) $89 \mathrm { nC }$
C) $22 \mathrm { nC }$
D) $180 \mathrm { nC }$
E) $45 \mathrm { nC }$

Question 71

Write the word or phrase that best completes each statement or answers the question.
If a point charge of $- 30 \mu \mathrm { C }$ experiences an electrostatic upward force of $27 \mathrm { mN }$ at a certain Iocation in the laboratory, what are the magnitude and direction of the electric field at that location?

Question 72

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, charge $q _ { 1 } = 2.2 \times 10 ^ { - 6 } \mathrm { C }$ is placed at the origin and charge $q _ { 2 } = - 3.30 \times 10 ^ { - 6 } \mathrm { C }$ is placed on the $x$ -axis, at $x = - 0.200 \mathrm {~m}$ . Where along the $x$ -axis can a third charge $Q = - 8.30 \times 10 ^ { - 6 } \mathrm { C }$ be placed so that the resultant force on $Q$ is zero?

Question 73

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, the charge $Q$ is midway between two other charges. If $Q = - 7.5 \mathrm { nC }$ , what must be the charge $q 1$ so that charge $q 2$ remains stationary as $Q$ and $q 1$ are held in place?

A) $15 \mathrm { nC }$
B) $60 \mathrm { nC }$
C) $7.5 \mathrm { nC }$
D) $30 \mathrm { nC }$

Question 74

Choose the one alternative that best completes the statement or answers the question.
What is the magnitude of a the vertical electric field that will balance the weight of a plastic sphere of mass $2.1 \mathrm {~g}$ that has been charged to $- 3.0 \mathrm { nC }$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $1.5 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$
B) $6.9 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$
C) $7.8 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { C }$
D) $2.1 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$

Question 75

Write the word or phrase that best completes each statement or answers the question.
A point charge $Q = - 12 \mu \mathrm { C }$ , and two other charges $q _ { 2 }$ and $q _ { 2 }$ , are placed on $x - y$ axes as shown in the figure. The electric force components on charge $Q$ are $F _ { x } = + 0.005 \mathrm {~N}$ and $F _ { y } =$ $- 0.003 \mathrm {~N} . \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right)$
(a) How many excess electrons are there in charge $Q$ ?
(b) What are the charges $q 1$ and q2, including their signs?

Question 76

Choose the one alternative that best completes the statement or answers the question.
An electron is projected with an initial velocity $v _ { 0 } = 8.4 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ along the $y$ -axis, which is the centerline between a pair of charged plates, as shown in the figure. The plates are $1.0 \mathrm {~m}$ long and are separated by $0.10 \mathrm {~m}$ . 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? $\left( e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right.$ , $m _ { \text {electron } } = 9.11 \times 10 - 31 \mathrm {~kg}$ )

A) $35,000 \mathrm {~N} / \mathrm { C }$
B) $29,000 \mathrm {~N} / \mathrm { C }$
C) $40,000 \mathrm {~N} / \mathrm { C }$
D) $51,000 \mathrm {~N} / \mathrm { C }$
E) $45,000 \mathrm {~N} / \mathrm { C }$

Question 77

Write the word or phrase that best completes each statement or answers the question.
There is $\mathrm { a } + 5.0 - \mu \mathrm { C }$ charge at three corners of a square having sides $70 \mathrm {~mm}$ long. What are the magnitude and direction of the net electrostatic force on $+ 6.0 \mu \mathrm { C }$ placed at the center of the square? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 78

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, three small charges are equally spaced on the arc of a circle that is centered at the charge $Q$ , where $Q = + 23 \mathrm { nC }$ 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 three charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $1.7 \times 10 ^ { - 4 } \mathrm {~N}$
B) $2.6 \times 10 ^ { - 4 } \mathrm {~N}$
C) $2.1 \times 10 ^ { - 4 } \mathrm {~N}$
D) $3.1 \times 10 ^ { - 4 } \mathrm {~N}$

Question 79

Write the word or phrase that best completes each statement or answers the question.
Two point charges $q = - 8.50 \mu \mathrm { C }$ are fixed $10.0 \mathrm {~cm}$ apart along a horizontal bar, as shown in the figure. Their electrical forces will be used to balance the weight of a very small sphere carrying a charge $Q = + 15.0 \mu \mathrm { C } , 10.0 \mathrm {~cm}$ from each of them in a place where $g = 9.80 \mathrm {~m} / \mathrm { s } 2$ . What is the greatest mass $M$ this sphere can have without falling? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \right.$ $\left. \mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 80

Choose the one alternative that best completes the statement or answers the question.
A small styrofoam ball of mass $0.120 \mathrm {~g}$ is placed in an electric field of $6000 \mathrm {~N} / \mathrm { C }$ pointing downward. What excess charge must be placed on the ball for it to remain suspended in the field?

A) $- 57.2 \mathrm { nC }$
B) $- 18.0 \mathrm { nC }$
C) $- 196 \mathrm { nC }$
D) $- 125 \mathrm { nC }$
E) $- 16.0 \mathrm { nC }$