Deck 18: Electric Forces and Electric Fields

Question 1

Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other.While a negatively charged rod is held near, but not touching sphere A, someone moves ball B away from A.How will the spheres be charged, if at all?

A)
B)
C)
D)
E)

Answer 1

Question 2

Consider three identical metal spheres, A, B, and C.Sphere A carries a charge of -2.0 µC; sphere B carries a charge of -6.0 µC; and sphere C carries a charge of +4.0 µC.Spheres A and B are touched together and then separated.Spheres B and C are then touched and separated.Does sphere C end up with an excess or a deficiency of electrons and how many electrons is it?

A)deficiency, 6 × 10¹³
B)excess, 3 × 10¹³
C)excess, 2 × 10¹³
D)deficiency, 3 × 10¹²
E)There is no excess or deficiency of electrons.

Answer 2

There is no excess or deficiency of electrons.

Question 3

Four point charges, each of the same magnitude, with varying signs are arranged at the corners of a square as shown.Which of the arrows labeled A, B, C, and D gives the correct direction of the net force that acts on the charge at the upper right corner?

A)A
B)B
C)C
D)D
E)The net force on that charge is zero.

Answer 3

B

Question 4

Determine the ratio of the electrostatic force to the gravitational force between a proton and an electron, F_E/F_G.Note: k = 8.99 × 10⁹ N-m²/C²; G = 6.672 × 10^-11 N-m²/kg²; m_e = 9.109 × 10^-31 kg; and m_p = 1.672 × 10^-27 kg.

A)1.24 × 10²³
B)2.52 × 10²⁹
C)1.15 × 10³¹
D)2.26 × 10³⁹
E)1.42 × 10⁵⁸

Question 5

Complete the following statement: When a glass rod is rubbed with silk cloth, the rod becomes positively charged as

A)positive charges are transferred from the silk to the rod.
B)negative charges are transferred from the rod to the silk.
C)positive charges are created on the surface of the rod.
D)negative charges are transferred from the silk to the rod.
E)positive charges are transferred from the rod to the silk.

Question 6

A charged conductor is brought near an uncharged insulator.Which one of the following statements is true?

A)Both objects will repel each other.
B)Both objects will attract each other.
C)Neither object exerts an electrical force on the other.
D)The objects will repel each other only if the conductor has a negative charge.
E)The objects will attract each other only if the conductor has a positive charge.

Question 7

One mole of a substance contains 6.02 × 10²³ protons and an equal number of electrons.If the protons could somehow be separated from the electrons and placed in very small, individual containers separated by a million meters, what would be the magnitude of the electrostatic force exerted by one box on the other?

A)8.7 × 10³ N
B)9.5 × 10⁴ N
C)2.2 × 10⁵ N
D)8.4 × 10⁷ N
E)1.6 × 10⁸ N

Question 8

Two charged particles A and B are located near one another.Both the magnitude and direction of the force that particle A exerts on particle B is independent of

A)the sign of charge B.
B)the sign of charge A.
C)the distance between A and B.
D)the magnitude of the charge on B.
E)The magnitude and direction of the force are dependent on all of the above choices.

Question 9

An aluminum nail has an excess charge of +3.2 µC.How many electrons must be added to the nail to make it electrically neutral?

A)2.0 × 10¹³
B)2.0 × 10¹⁹
C)3.2 × 10¹⁶
D)3.2 × 10⁶
E)5.0 × 10^-14

Question 10

Each of three objects has a net charge.Objects A and B attract one another.Objects B and C also attract one another, but objects A and C repel one another.Which one of the following table entries is a possible combination of the signs of the net charges on these three objects?

A)
B)
C)
D)
E)

Question 11

A -4.0-µC charge is located 0.45 m to the left of a +6.0-µC charge.What is the magnitude and direction of the electrostatic force on the positive charge?

A)2.2 N, to the right
B)2.2 N, to the left
C)1.1 N, to the right
D)1.1 N, to the left
E)4.4 N, to the right

Question 12

Two positive point charges Q and 2Q are separated by a distance R.If the charge Q experiences a force of magnitude F when the separation is R, what is the magnitude of the force on the charge 2Q when the separation is 2R ?

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

Question 13

Three charges are positioned as indicated in the figure.What are the horizontal and vertical components of the net force exerted on the +15 µC charge by the +11 µC and +13 µC charges?

A)
B)
C)
D)
E)

Question 14

A conducting sphere has a net charge of -6.4 × 10^-17 C.What is the approximate number of excess electrons on the sphere?

A)100
B)200
C)300
D)400
E)500

Question 15

Which one of the following statements best explains why tiny bits of paper are attracted to a charged rubber rod?

A)Paper is naturally a positive material.
B)Paper is naturally a negative material.
C)The paper becomes electrically polarized by induction.
D)Rubber and paper always attract each other.
E)The paper acquires a net positive charge by induction.

Question 16

Two uncharged, conducting spheres, A and B, are held at rest on insulating stands and are in contact.A positively charged rod is brought near sphere A as suggested in the figure.While the rod is in place, someone moves sphere B away from A.How will the spheres be charged, if at all?

A)
B)
C)
D)
E)

Question 17

A charge Q exerts a 1.2 N force on another charge q.If the distance between the charges is doubled, what is the magnitude of the force exerted on Q by q?

A)0.30 N
B)0.60 N
C)2.4 N
D)3.6 N
E)4.8 N

Question 18

Complete the following statement: When an ebonite rod is rubbed with animal fur, the rod becomes negatively charged as

A)positive charges are transferred from the fur to the rod.
B)negative charges are transferred from the rod to the fur.
C)negative charges are created on the surface of the rod.
D)negative charges are transferred from the fur to the rod.
E)positive charges are transferred from the rod to the fur.

Question 19

Five styrofoam balls are suspended from insulating threads.Several experiments are performed on the balls; and the following observations are made: What are the charges, if any, on each ball?

A)
B)
C)
D)
E)

Question 20

At what separation will two charges, each of magnitude 6.0 $\mu$ C, exert a force of 0.70 N on each other?

A)1.1 × 10^-5 m
B)0.23 m
C)0.48 m
D)0.68 m
E)1.4 m

Question 21

18-2
Five particles are shot from the left into a region that contains a uniform electric field.The numbered lines show the paths taken by the five particles.A negatively charged particle with a charge -3Q follows path 2 while it moves through this field.Do not consider any effects due to gravity.
In which direction does the electric field point?

A)toward the top of the page
B)toward the left of the page
C)toward the right of the page
D)toward the bottom of the page
E)out of the page, toward the reader

Question 22

18-1
The figure shows an equilateral triangle ABC.A positive point charge +q is located at each of the three vertices A, B, and C.Each side of the triangle is of length a.A point charge Q (that may be positive or negative) is placed at the mid-point between B and C.
Is it possible to choose the value of Q (that is non-zero) such that the force on Q is zero? Explain why or why not.

A)Yes, because the forces on Q are vectors and three vectors can add to zero.
B)No, because the forces on Q are vectors and three vectors can never add to zero.
C)Yes, because the electric force at the mid-point between B and C is zero whether a charge is placed there or not.
D)No, because the forces on Q due to the charges at B and C point in the same direction.
E)No, because a fourth charge would be needed to cancel the force on Q due to the charge at A.

Question 23

18-2
Five particles are shot from the left into a region that contains a uniform electric field.The numbered lines show the paths taken by the five particles.A negatively charged particle with a charge -3Q follows path 2 while it moves through this field.Do not consider any effects due to gravity.
What is the magnitude of the electric field due to a 6.0 × 10^-9 C charge at a point located 0.025 m from the charge?

A)8.6 × 10² N/C
B)1.2 × 10⁴ N/C
C)1.8 × 10⁵ N/C
D)3.6 × 10⁶ N/C
E)7.2 × 10⁷ N/C

Question 24

Which one of the following statements is true concerning the strength of the electric field between two oppositely charged parallel plates?

A)It is zero midway between the plates.
B)It is a maximum midway between the plates.
C)It is a maximum near the positively charged plate.
D)It is a maximum near the negatively charged plate.
E)It is constant between the plates except near the edges.

Question 25

Two particles of the same mass carry charges +3Q and -2Q, respectively.They are shot into a region that contains a uniform electric field as shown.The particles have the same initial velocities in the positive x direction.The lines, numbered 1 through 5, indicate possible paths for the particles.If the electric field points in the negative y direction, what will be the resulting paths for these particles?

A)path 1 for +3Q and path 4 for -2Q
B)path 3 for +3Q and path 2 for -2Q
C)path 4 for +3Q and path 3 for -2Q
D)path 2 for +3Q and path 5 for -2Q
E)path 5 for +3Q and path 2 for -2Q

Question 26

If a +2.0 × 10^-5 C point charge is placed at P, what is the force exerted on it?

A)0.2 N, toward the negative plate
B)0.2 N, toward the positive plate
C)5 × 10⁴ N, toward the positive plate
D)5 × 10⁴ N, toward the negative plate
E)5 × 10⁴ N, into the plane of the page

Question 27

At which point (or points) is the electric field zero N/C for the two point charges shown on the x axis?

A)The electric field is never zero in the vicinity of these charges.
B)The electric field is zero somewhere on the x axis to the left of the +4q charge.
C)The electric field is zero somewhere on the x axis to the right of the -2q charge.
D)The electric field is zero somewhere on the x axis between the two charges, but this point is nearer to the -2q charge.
E)The electric field is zero at two points along the x axis; one such point is to the right of the -2q charge and the other is to the left of the +4q charge.

Question 28

An electron traveling horizontally enters a region where a uniform electric field is directed upward.What is the direction of the force exerted on the electron once it has entered the field?

A)to the left
B)to the right
C)upward
D)downward
E)out of the page, toward the reader

Question 29

18-2
Five particles are shot from the left into a region that contains a uniform electric field.The numbered lines show the paths taken by the five particles.A negatively charged particle with a charge -3Q follows path 2 while it moves through this field.Do not consider any effects due to gravity.
Which path would be followed by a charge +6Q?

A)path 1
B)path 2
C)path 3
D)path 4
E)path 5

Question 30

Four point charges are held fixed at the corners of a square as shown in the figure.Which of the five arrows shown below most accurately shows the direction of the net force on the charge -Q due to the presence of the three other charges?

A)a
B)b
C)c
D)d
E)e

Question 31

Three charges are located along the x axis as shown in the drawing.The mass of the -1.2 µC is 4.0 × 10^-9 kg.Determine the magnitude and direction of the acceleration of the -1.2 µC charge when it is allowed to move if the other two charges remain fixed.

A)2 × 10⁵ m/s², to the right
B)1 × 10⁵ m/s², to the left
C)7 × 10⁴ m/s², to the right
D)3 × 10⁵ m/s², to the left
E)4 × 10⁶ m/s², to the right

Question 32

Complete the following statement: The magnitude of the electric field at a point in space does not depend upon

A)the distance from the charge causing the field.
B)the sign of the charge causing the field.
C)the magnitude of the charge causing the field.
D)the force that a unit positive charge will experience at that point.
E)the force that a unit negative charge will experience at that point.

Question 33

In Frame 1, two identical conducting spheres, A and B, carry equal amounts of excess charge that have the same sign.The spheres are separated by a distance d; and sphere A exerts an electrostatic force on sphere B that has a magnitude F.A third sphere, C, which is handled only by an insulating rod, is introduced in Frame 2.Sphere C is identical to A and B except that it is initially uncharged.Sphere C is touched first to sphere A, in Frame 2, and then to sphere B, in Frame 3, and is finally removed in Frame 4. Determine the magnitude of the electrostatic force that sphere A exerts on sphere B in Frame 4.

A)F/2
B)F/3
C)3F/4
D)3F/8
E)zero

Question 34

18-2
Five particles are shot from the left into a region that contains a uniform electric field.The numbered lines show the paths taken by the five particles.A negatively charged particle with a charge -3Q follows path 2 while it moves through this field.Do not consider any effects due to gravity.
Which path would be followed by a helium atom (an electrically neutral particle)?

A)path 1
B)path 2
C)path 3
D)path 4
E)path 5

Question 35

18-3
The figure shows a parallel plate capacitor.The surface charge density on each plate is 8.8 × 10^-8 C/m².The point P is located 1.0 × 10^-5 m away from the positive plate.
Which one of the following statements concerning the direction of the electric field between the plates is true?

A)It points to the left.
B)It points to the right.
C)It points toward the negative plate.
D)It points toward the positive plate.
E)It points up out of the plane of the page.

Question 36

Which one of the following statements is true concerning the magnitude of the electric field at a point in space?

A)It is a measure of the total charge on the object.
B)It is a measure of the electric force on any charged object.
C)It is a measure of the ratio of the charge on an object to its mass.
D)It is a measure of the electric force per unit mass on a test charge.
E)It is a measure of the electric force per unit charge on a test charge.

Question 37

What is the magnitude of the electric field at the point P?

A)8.8 N/C
B)88 N/C
C)1.0 × 10² N/C
D)8.8 × 10² N/C
E)9.9 × 10³ N/C

Question 38

In the figure, point A is a distance L away from a point charge Q.Point B is a distance 4L away from Q.What is the ratio of the electric field at B to that at A, E_B/E_A?

A)1/16
B)1/9
C)1/4
D)1/3
E)This cannot be determined since neither the value of Q nor the length L is specified.

Question 39

A small sphere of mass 2.5 × 10^-5 kg carries a total charge of 6.0 × 10^-8 C.The sphere hangs from a silk thread between two large parallel conducting plates.The excess charge on each plate is equal in magnitude, but opposite in sign.If the thread makes an angle of 30° with the positive plate as shown, what is the magnitude of the charge density on each plate?

A)2.5 × 10^-9 C/m²
B)5.2 × 10^-9 C/m²
C)1.0 × 10^-9 C/m²
D)2.1 × 10^-8 C/m²
E)4.2 × 10^-8 C/m²

Question 40

Four point charges are placed at the corners of a square as shown in the figure.Each side of the square has length 2.0 m.Determine the magnitude of the electric field at the point P, the center of the square.

A)2.0 × 10^-6 N/C
B)3.0 × 10^-6 N/C
C)9.0 × 10³ N/C
D)1.8 × 10⁴ N/C
E)2.7 × 10⁴ N/C

Question 41

An electric dipole is released from rest in a uniform electric field with the orientation shown.Which entry in the table below correctly describes the net torque and the net force on the dipole?

A)
B)
C)
D)
E)

Question 42

Two identical conducting spheres carry charges of +5.0 $\mu$ C and -1.0 $\mu$ C, respectively.The centers of the spheres are initially separated by a distance L.The two spheres are brought together so that they are in contact.The spheres are then returned to their original separation L.What is the ratio of the magnitude of the electric force on either sphere after the spheres are touched to that before they were touched?

A)1/1
B)4/5
C)9/5
D)5/1
E)4/9

Question 43

A solid, conducting sphere of radius a carries an excess charge of +6 µC.This sphere is located at the center of a hollow, conducting sphere with an inner radius of b and an outer radius of c as shown.The hollow sphere also carries a total excess charge of +6 µC.

-Determine the excess charge on the outer surface of the outer sphere (a distance c from the center of the system).

A)zero coulombs
B)-6 $\mu$ C
C)+6 $\mu$ C
D)+12 $\mu$ C
E)-12 $\mu$ C

Question 44

A cubical Gaussian surface is placed in a uniform electric field as shown in the figure.The length of each edge of the cube is 1.0 m.The uniform electric field has a magnitude of 5.0 × 10⁸ N/C and passes through the left and right sides of the cube perpendicular to the surface.What is the total electric flux that passes through the cubical Gaussian surface?

A)5.0 × 10⁸ N.m²/C
B)3.0 × 10⁹ N.m²/C
C)2.5 × 10⁶ N.m²/C
D)1.5 × 10⁷ N.m²/C
E)zero N.m²/C

Question 45

A helium nucleus is located between the plates of a parallel-plate capacitor as shown.The nucleus has a charge of +2e and a mass of 6.6 × 10^-27 kg.What is the magnitude of the electric field such that the electric force exactly balances the weight of the helium nucleus so that it remains stationary?

A)4.0 × 10^-7 N/C
B)6.6 × 10^-26 N/C
C)2.0 × 10^-7 N/C
D)5.0 × 10^-3 N/C
E)1.4 × 10^-8 N/C

Question 46

The magnitude of the electric field at a distance of two meters from a negative point charge is E.What is the magnitude of the electric field at the same location if the magnitude of the charge is doubled?

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

Question 47

What is the magnitude and direction of the electric force on a -3.0 µC charge at a point where the electric field is 2800 N/C and is directed along the +y axis.

A)0.018 N, -y direction
B)0.012 N, +y direction
C)0.0084 N, -y direction
D)0.0056 N, +y direction
E)0.022 N, +x direction

Question 48

The figure shows the electric field lines in the vicinity of two point charges.Which one of the following statements concerning this situation is true?

A)q₁ is negative and q₂ is positive.
B)The magnitude of the ratio (q₂/ q₁)is less than one.
C)Both q₁and q₂ have the same sign of charge.
D)The magnitude of the electric field is the same everywhere.
E)The electric field is strongest midway between the charges.

Question 49

A circular loop of wire with a diameter of 0.626 m is rotated in a uniform electric field to a position where the electric flux through the loop is a maximum.At this position, the electric flux is 7.50 × 10⁵ N.m²/C.Determine the magnitude of the electric field.

A)8.88 × 10⁵ N/C
B)1.07 × 10⁶ N/C
C)2.44 × 10⁶ N/C
D)4.24 × 10⁶ N/C
E)6.00 × 10⁶ N/C

Question 50

Which one of the following statements is true concerning the spacing of the electric field lines in the vicinity of two point charges of equal magnitude and opposite sign?

A)The spacing indicates the direction of the electric field.
B)The spacing does not depend on the magnitude of the charges.
C)The spacing is large when the magnitude of the charges is large.
D)The spacing indicates the relative magnitude of the electric field.
E)The spacing is small when the magnitude of the charges is small.

Question 51

18-4
Two point charges, A and B, lie along a line separated by a distance L.The point x is the midpoint of their separation.
Which combination of charges will yield zero electric field at the point x?

A)+1q and -1q
B)+2q and -3q
C)+1q and -4q
D)-1q and +4q
E)+4q and +4q

Question 52

Which one of the following statements is true concerning the electrostatic charge on a conductor?

A)The charge is uniformly distributed throughout the volume.
B)The charge is confined to the surface and is uniformly distributed.
C)Most of the charge is on the outer surface, but it is not uniformly distributed.
D)The charge is entirely on the surface and it is distributed according to the shape of the object.
E)The charge is dispersed throughout the volume of the object and distributed according to the object's shape.

Question 53

18-4
Two point charges, A and B, lie along a line separated by a distance L.The point x is the midpoint of their separation.
Which combination of charges would yield the greatest repulsive force between the charges?

A)-2q and -4q
B)+1q and -3q
C)-1q and -4q
D)-2q and +4q
E)+1q and +7q

Question 54

A solid, conducting sphere of radius a carries an excess charge of +6 µC.This sphere is located at the center of a hollow, conducting sphere with an inner radius of b and an outer radius of c as shown.The hollow sphere also carries a total excess charge of +6 µC.

-Determine the excess charge on the inner surface of the outer sphere (a distance b from the center of the system).

A)zero coulombs
B)-6 $\mu$ C
C)+6 $\mu$ C
D)+12 $\mu$ C
E)-12 $\mu$ C

Question 55

A straight, copper wire has a length of 0.50 m and an excess charge of -1.0 × 10^-5 C distributed uniformly along its length.Find the magnitude of the electric field at a point located 7.5 × 10^-3 m from the midpoint of the wire.

A)1.9 × 10¹⁰ N/C
B)1.5 ×10⁶ N/C
C)6.1 × 10¹³ N/C
D)7.3 × 10⁸ N/C
E)4.8 × 10⁷ N/C

Question 56

What is the electric flux passing through a Gaussian surface that surrounds a +0.075 C point charge?

A)8.5 × 10⁹ N.m²/C
B)6.8 × 10⁸ N.m²/C
C)1.3 × 10⁷ N.m²/C
D)4.9 × 10⁶ N.m²/C
E)7.2 × 10⁵ N.m²/C

Question 57

A conducting sphere carries a net charge of +6 µC.The sphere is located at the center of a conducting spherical shell that carries a net charge of -2 µC.Determine the excess charge on the outer surface of the spherical shell.

A)-4 µC
B)+4 µC
C)-8 µC
D)+8 µC
E)+6 µC

Question 58

A uniform electric field with a magnitude of 125 000 N/C passes through a rectangle with sides of 2.50 m and 5.00 m.The angle between the electric field vector and the vector normal to the rectangular plane is 65.0°.What is the electric flux through the rectangle?

A)1.56 × 10⁶ N.m²/C
B)6.60 × 10⁵ N.m²/C
C)1.42 × 10⁵ N.m²/C
D)5.49 × 10⁴ N.m²/C
E)4.23 × 10⁴ N.m²/C

Question 59

A rigid electric dipole is free to move in the electric field represented in the figure.Which one of the following phrases most accurately describes the initial motion of the dipole if it is released from rest in the position shown?

A)It moves to the left.
B)It moves to the right.
C)It does not move at all.
D)It moves toward to the top of the page.
E)It moves toward the bottom of the page.

Question 60

A total charge of -6.50 µC is uniformly distributed within a sphere that has a radius of 0.150 m.What is the magnitude and direction of the electric field at 0.300 m from the surface of the sphere?

A)2.89 × 10⁵ N/C, radially inward
B)6.49 × 10⁵ N/C, radially outward
C)4.69 × 10⁵ N/C, radially inward
D)9.38 × 10⁵ N/C, radially outward
E)1.30 × 10⁶ N/C, radially inward

Question 61

Which one of the following figures shows a qualitatively accurate sketch of the electric field lines in and around this system?

A)a
B)b
C)c
D)d
E)e