Deck 21: The Electric Field I: Discrete Charge Distributions

Question 1

Two small spheres attract one another electrostatically.This can occur for a variety of reasons.Which of the following statements must be true?

A)at least one sphere is charged
B)neither is charged
C)both are charged
D)both have the same charge
E)None of these is correct.

Answer 1

at least one sphere is charged

Question 2

Experimental evidence indicates that

A)charge is quantized and conserved.
B)charge is quantized but not conserved.
C)charge is conserved but not quantized.
D)charge is neither quantized nor conserved.
E)None of these answers is correct.

Answer 2

charge is quantized and conserved.

Question 3

Electric charges of the opposite sign

A)also have the same magnitude.
B)attract each other.
C)exert no forces on each other.
D)repel each other.
E)None of these is correct.

Answer 3

attract each other.

Question 4

Electrons

A)are about 2000 times more massive than protons.
B)are about 2000 times less massive than protons.
C)have 2000 times the charge of protons.
D)have 1/2000 the charge of protons.
E)can have any amount of charge.

Question 5

A positive charge of 94.0 nC is 12.0 cm from a negative charge of 53.0 nC.The force on one of the charges due to the other is approximately

A)1.13 mN
B)0.373 mN
C)3.11 mN
D)1.25 mN
E)1.02 $\mu$ N

Question 6

Charges q₁ and q₂ exert repulsive forces of 15 N on each other.What is the repulsive force when their separation is increased so that their final separation is 160% of their initial separation?

A)1.3 N
B)5.9 N
C)9.8 N
D)8.7 N
E)6.4 N

Question 7

Two positive charges (+8.0 mC and +2.0 mC)are separated by 300 m.A third charge is placed at distance r from the +8.0 mC charge in such a way that the resultant electric force on the third charge due to the other two charges is zero.The distance r is

A)0.25 km
B)0.20 km
C)0.15 km
D)0.13 km
E)0.10 km

Question 8

Point charges of 4.0 $\times$ 10^-8 C and -2.0 $\times$ 10^-8 C are placed 12 cm apart.A third point charge of 3.0 $\times$ 10^-8 C halfway between the first two point charges experiences a force of magnitude

A)4.5 $\times$ 10^-3 N
B)2.0 $\times$ 10^-3 N
C)1.5 $\times$ 10^-3 N
D)zero
E)5.0 $\times$ 10^-3 N

Question 9

How many electrons must be transferred to a body to produce a charge of 125 nC?

A)1.25 $\times$ 10^-7
B)1.60 $\times$ 10^-19
C)1.28 $\times$ 10¹²
D)3.45 $\times$ 10¹¹
E)7.81 $\times$ 10¹¹

Question 10

Protons

A)are about 2000 times more massive than electrons.
B)are about 2000 times less massive than electrons.
C)have 2000 times the charge of electrons.
D)have 1/2000 the charge of electrons.
E)can have any amount of charge.

Question 11

Which of the following statements about conductors and insulators is NOT correct?

A)Charges can move freely in conductors.
B)Charges can move freely in insulators.
C)In conductors,one or more of the outer electrons from an atom is no longer bounded to the atom.
D)In insulators,all the electrons from an atom are bounded to the atom.
E)Charges in both conductors and insulators can become polarized,i.e.,one end has charges of one sign and the other end has charges of opposite sign.

Question 12

A particular nucleus of the element erbium contains 68 protons and 90 neutrons.What is the total number of electrons in the neutral erbium atom?

A)90
B)158
C)22
D)68
E)None of the above

Question 13

Electric charges of the same sign

A)also have the same magnitude.
B)attract each other.
C)repel each other.
D)exert no forces on each other.
E)None of these is correct.

Question 14

Three charges are located at 100-m intervals along a horizontal line: a charge of -3.0 C on the left,+2.0 C in the middle,and +1.0 C on the right.What is the resultant force on the 1.0 C charge due to the other two?

A)1.1 $\times$ 10⁶ N to the right
B)1.1 $\times$ 10⁶ N to the left
C)2.5 $\times$ 10⁶ N to the right
D)2.5 $\times$ 10⁶ N to the left
E)4.5 $\times$ 10⁷ N to the right

Question 15

Charges q₁ and q₂ exert repulsive forces of 10 N on each other.What is the repulsive force when their separation is decreased so that their final separation is 80% of their initial separation?

A)16 N
B)12 N
C)10 N
D)8.0 N
E)6.4 N

Question 16

Two small spheres repel one another electrostatically.Which of the following statements must be true?

A)both have the same charge
B)neither is charged
C)both are charged
D)at least one sphere is charged
E)they are oppositely charged

Question 17

A particular nucleus of the element erbium contains 68 protons and 90 neutrons.What is the total charge of the erbium nucleus?

A)zero
B)1.4 $\times$ 10^-17 C
C)2.5 $\times$ 10^-17 C
D)1.1 $\times$ 10^-17 C
E)3.5 $\times$ 10^-18 C

Question 18

An electron (q =+e)and a positron (q = +e)can combine to give off two gamma rays.The net change in the algebraic sum of the charges is

A)+2e
B)zero
C)-2e
D)+e
E)-e

Question 19

If an object is determined to have a negative charge of 160 nC,you can conclude that the object has an excess of

A)10⁹ electrons
B)10¹⁰ electrons
C)10¹¹ electrons
D)10¹² electrons
E)10¹³ electrons

Question 20

A positive charge of 63.0 nC is 15.0 cm from a negative charge of 45.0 nC.The force on one of the charges due to the other is approximately

A)1.13 $\times$ 10^-3 N
B)1.13 $\times$ 10^-7 N
C)1.02 $\times$ 10⁷ N
D)1.25 $\times$ 10^-13 N
E)1.02 $\times$ 10^-6 N

Question 21

Three charges are located at 100-m intervals along a horizontal line: a charge of -3.0 C on the left,2.0 C in the middle,and 1.0 C on the right.What is the electric field on the horizontal line halfway between the -3.0 C and 2.0 C charges?

A)2.2 $\times$ 10⁷ N/C to the left
B)1.8 $\times$ 10⁷ N/C to the right
C)1.8 $\times$ 10⁷ N/C to the left
D)3.2 $\times$ 10⁶ N/C to the right
E)4.0 $\times$ 10⁶ N/C to the left

Question 22

A positive charge that is in an electric field experiences a force that is

A)perpendicular to .
B)zero because the speed is zero.
C)in the direction opposite to .
D)in the same direction as .
E)None of these is correct.

Question 23

Coulomb's law and Newton's law of gravitation both involve which of the following?

A)the mass of the particle
B)the charge on the particle
C)permeability
D)permittivity
E)the inverse-square law

Question 24

Which of the following statements is not true?

A)In nature,electric charge is conserved.
B)The force of repulsion between two like charges is directly proportional to the product of the square of the charges.
C)The force of repulsion between two like charges is inversely proportional to the square of the distance separating the charges.
D)Unlike charges attract each other.
E)Like charges repel each other.

Question 25

The SI units of electric fields can be expressed as

A)C/m²
B)C/s
C)V · C
D)N
E)V/m

Question 26

The direction of the electric field at a point is the same as

A)the force on a neutron placed at that point.
B)the force on a proton placed at that point.
C)the force on an electron placed at that point.
D)the force on a hydrogen molecule placed at that point.
E)None of these is correct.

Question 27

The Coulomb's force between a proton and an electron is 2.27 $\times$ 10³⁹ times greater than the gravitational force.If the two forces were equal,what should the size of the elementary charge be

A)1.60 $\times$ 10^-19 C
B)3.36 $\times$ 10^-39 C
C)1.23 $\times$ 10^-77 C
D)2.27 $\times$ 10^-39 C
E)4.41 $\times$ 10^-40 C

Question 28

The force between two very small charged bodies is found to be F.If the distance between them is doubled without altering their charges,the force between them becomes

A)F/2
B)2F
C)F/4
D)4F
E)1/F²

Question 29

An electric field with a magnitude of 6.0 $\times$ 10⁴ N/C is directed parallel to the positive y axis.A particle with a charge q = 4.8 $\times$ 10^-19 C is moving along the x axis with a speed v = 3.0 $\times$ 10⁶ m/s.The force on the charge is approximately

A)8.6 $\times$ 10^-8 N perpendicular to the xy plane.
B)2.9 $\times$ 10^-14 N in the y direction.
C)8.6 $\times$ 10^-8 N in the x direction.
D)zero.
E)2.9 $\times$ 10^-14 N in the x direction.

Question 30

An electron is moving horizontally east in an electric field that points vertically upward.The electric force on the proton is

A)zero.
B)upward.
C)downward.
D)to the west.
E)to the east.

Question 31

The force between two very small charged bodies is found to be F.If the distance between them is tripled without altering their charges,the force between them becomes

A)9F
B)3F
C)F/3
D)F/9
E)1/F³

Question 32

A particular nucleus of the element plutonium contains 94 protons and 150 neutrons.What is the magnitude of the force from the nucleus on a single electron that is at a distance of 0.563 $\times$ 10^-12 m from the plutonium nucleus?

A)4.27 $\times$ 10¹⁵ N
B)3.85 $\times$ 10^-14 N
C)6.83 $\times$ 10^-2 N
D)6.42 N
E)1.09 $\times$ 10^-1 N

Question 33

Two charges of the same magnitude and sign are placed a certain distance apart.There is only one point in space near them where the electric field is zero.Which,if any,of the following statements about that point is true?

A)It cannot be on the line joining the charges.
B)It must be on the line joining the charges and between the charges.
C)It must be on the line joining the charges but not between the charges.
D)Its position depends on the size of the charges.
E)None of these is correct.

Question 34

Two point charges of unknown magnitude and sign are a distance d apart.If the electric field strength is zero at a point between them on the line joining them,you can conclude that

A)the charges are equal in magnitude but opposite in sign.
B)the charges are equal in magnitude and have the same sign.
C)the charges are not necessarily equal in magnitude but have opposite signs.
D)the charges are not necessarily equal in magnitude but have the same sign.
E)there is not enough information to say anything specific about the charges.

Question 35

Two charges Q₁ and Q₂ are a distance d apart.If the electric field is zero at a distance of 3d/4 from Q₁ (towards Q₂),then what is the relation between Q₁ and Q₂?

A)Q₁ = Q₂ /9
B)Q₁ = 9Q₂
C)Q₁ = Q₂ /3
D)Q₁ = 3Q₂
E)Q₁ = 4Q₂ /3

Question 36

Two electrons are separated by a distance of 1.6 nm.Each experiences an electrostatic force of approximately

A)9.0 $\times$ 10⁹ N
B)1.1 $\times$ 10^-32 N
C)9.0 $\times$ 10²⁰ N
D)1.0 $\times$ 10^-22 N
E)9.0 $\times$ 10^-11 N

Question 37

A proton is about 2000 times more massive that an electron but they both have charges of the same magnitude.The magnitude of the force on an electron by a proton is ____ the magnitude of the force on the proton by the electron.

A)2000 times greater than
B)equal to
C)2000 times less than
D)negligible compared to
E)None of these answers is correct.

Question 38

A proton is moving horizontally north in an electric field that points vertically upward.The electric force on the proton is

A)zero.
B)upward.
C)downward.
D)to the west.
E)to the east.

Question 39

Two charges Q₁ and Q₂ are distance d apart.If the electric field is zero at distance 3d/2 from Q₁ and d/2 from Q₂,along the line joining Q₁ and Q₂,then what is the relation between Q₁ and Q₂?

A)Q₁ = 9Q₂
B)Q₁ = -Q₂ /9
C)Q₁ = Q₂ /3
D)Q₁ = -3Q₂
E)Q₁ = -9Q₂

Question 40

A particular nucleus of the element plutonium contains 94 protons and 150 neutrons.What is the magnitude of the electric field at a distance of 0.563 $\times$ 10^-12 m from the nucleus?

A)6.81 $\times$ 10¹⁷ N/C
B)4.27 $\times$ 10¹⁷ N/C
C)2.40 $\times$ 10⁵ N/C
D)3.83 $\times$ 10⁵ N/C
E)none of the above

Question 41

Which of the following statements about electric field lines are true?

A)The lines are drawn symmetrically entering or leaving an isolated charge.
B)At large distances from a system of charges,the field lines are equally spaced and radial,as if they came from a single point charge equal to the net charge of the system.
C)Electric field lines begin on positive charges (or at infinity)and end on negative charges (or at infinity).
D)The number of lines leaving a positive charge or entering a negative charge is proportional to the charge.
E)All of these statements are true.

Question 42

An electric dipole p makes an angle of 30 ^$\circ$ with a uniform electric field of magnitude 300 N/C.If the torque on the dipole is 3.00 $\times$ 10^-12 N · m then calculate the magnitude of the dipole moment p.

A)2.00 $\times$ 10^-14 C · m
B)1.00 $\times$ 10^-14 C · m
C)4.00 $\times$ 10^-14 C · m
D)1.15 $\times$ 10^-14 C · m
E)1.73 $\times$ 10^-14 C · m

Question 43

Use the picture for the next problem. A negatively charged particle moving with speed v enters a region of uniform electric field E.

-If the charge q = 1 nC,mass m = 1 $\times$ 10^-14 kg,speed v = 10⁵ m/s,the electric field strength E = 2 $\times$ 10⁵ V/m,and width,w,of the electric field is 0.2 m,what is the speed of the particle when it emerges from the other side?

A)1.0 $\times$ 10⁵ m/s
B)4.0 $\times$ 10⁴ m/s
C)1.08 $\times$ 10⁵ m/s
D)1.4 $\times$ 10⁵ m/s
E)1.8 $\times$ 10⁵ m/s

Question 44

A point charge of +35 nC is above a point charge of -35 nC on a vertical line.The distance between the charges is 4.0 mm.What are the magnitude and direction of the dipole moment ?

A)zero
B)1.4 pC · m up
C)1.4 pC · m down
D)2.8 pC · m up
E)2.8 pC · m down

Question 45

Use the picture for the next problem.
A conducting sphere has a net charge of -q and of mass m is suspended from the ceiling by a light string.A uniform electric field E is applied vertical down on the sphere.
The tension T in the string is ____ the weight mg.

A)less than
B)equal to
C)greater than
D)dependent on the strength of E in relation to
E)insufficient information to tell

Question 46

An oil droplet of mass 1.00 $\times$ 10^-14 kg loses an electron while it is in an electric field of 1.00 $\times$ 10⁶ N/C.The resulting change in the acceleration of the oil droplet is approximately

A)1.76 $\times$ 10¹⁷ m/s²
B)16.0 m/s²
C)1.60 m/s²
D)1.76 $\times$ 10¹⁸ m/s²
E)176 m/s²

Question 47

Use the picture for the next problem.
A conducting sphere has a net charge of -q and of mass m is suspended from the ceiling by a light string.A uniform electric field E is applied vertical down on the sphere.

-If m = 1 g,q = 1 ^$\circ$ C and E = 5000 N/C,the tension T in the string is

A)5 $\times$ 10^-3 N
B)9.81 $\times$ 10^-3 N
C)4.81 $\times$ 10^-3 N
D)1.48 $\times$ 10^-2 N
E)0

Question 48

An electron is released from rest in a uniform electric field.If the electric field is 1.25 kN/C,at the end of 20 ns the electron's velocity will be approximately

A)2.5 $\times$ 10^-5 m/s
B)3.9 $\times$ 10³ m/s
C)3.0 $\times$ 10⁸ m/s
D)2.5 $\times$ 10³ m/s
E)4.4 $\times$ 10⁶ m/s

Question 49

Use the picture for the next problem. A negatively charged particle moving with speed v enters a region of uniform electric field E.
Using the direction compass on the right,the direction of the force on the charge is

A)1
B)2
C)3
D)4
E)There is no force on the charge.

Question 50

An electric dipole of magnitude 25 p C · m makes an angle of 65º with a uniform electric field of magnitude 3.0 $\times$ 10^-6 N/C.What is the magnitude of the torque on the dipole?

A)3.2 $\times$ 10^-16 N · m
B)6.2 $\times$ 10^-16 N · m
C)1.4 $\times$ 10^-15 N · m
D)6.8 $\times$ 10^-16 N · m
E)7.5 $\times$ 10^-16 N · m

Question 51

In a uniform electric field a proton has

A)a constant velocity in the direction of the field.
B)a constant velocity in a direction opposite to that of the field.
C)an approximately constant acceleration the direction of the field.
D)an approximately constant acceleration in a direction opposite to that of the field.
E)an approximately constant acceleration in a direction at right angles to the field.

Question 52

A molecule of HCl has a dipole moment of 3.39 $\times$ 10^-30 C · m.If we assume full donation of the hydrogen electron to the chlorine,then calculate the distance between the charge centers.

A)4.72 $\times$ 10¹⁰ m
B)1.06 $\times$ 10^-11 m
C)4.24 $\times$ 10^-11 m
D)2.12 $\times$ 10^-11 m
E)2.44 $\times$ 10^-11 m

Question 53

Which of the following statements about electric field lines is not true?

A)The number of lines leaving a positive charge or entering a negative charge is proportional to the charge.
B)The lines begin on positive charges and end on negative charges.
C)The density of the lines (the number per unit area perpendicular to the lines)is proportional to the magnitude of the field at that point.
D)Electric field lines cross midway between charges that have equal magnitude and sign.
E)The direction of each line indicates the direction that a positively charged particle would move if placed at that point in the electric field.

Question 54

An electron is released from rest in a uniform electric field.If the electric field is 3.65 kN/C,at the end of 15 ns the electron's velocity will be approximately

A)9.6 $\times$ 10⁶ m/s
B)3.9 $\times$ 10³ m/s
C)3.1 $\times$ 10⁸ m/s
D)5.5 $\times$ 10³ m/s
E)7.4 $\times$ 10⁶ m/s

Question 55

If nonelectric forces are negligible,a positively charged particle released from rest in a nonuniform electric field

A)moves perpendicular to the field with constant velocity.
B)moves with constant velocity parallel to the field.
C)accelerates in the direction of the field.
D)accelerates perpendicularly to the field.
E)moves only along equipotential lines.