Deck 21: Electrostatics

Question 1

Two ions are placed on the x-axis.One has a charge of +e and is located at the origin.The other has a charge of -4e and is located at x = +d,where d > 0.Where on the x-axis could a third charge be placed such that the net electrostatic force on it caused by the other two charges is zero?

A)x = -2d
B)x = -d
C)x = +d
D)x = +2d

Answer 1

x = -d

Question 2

Identical point charges Q are placed at each of the four corners of a 1.0 m* 2.0 m rectangle.If the magnitude of the electrostatic force on one of the charges is 28.5 N,what is the charge,Q of one of the four charges?

A)35 µC
B)68 µC
C)79 µC
D)83 µC
E)52 µC

Answer 2

52 µC

Question 3

Two point charges are placed on two of the corners of a triangle as shown.What magnitude of force would be felt by a 6.0 µC charge placed at the right angle?

A)10 N
B)24 N
C)32 N
D)44 N
E)58 N

Answer 3

32 N

Question 4

How many electrons does it take to make up 5.00 C of charge?

A)1.08 * 10¹⁹
B)1.17 * 10¹⁹
C)2.11 * 10¹⁹
D)3.12 * 10¹⁹
E)3.72 * 10¹⁹

Question 5

Two initially uncharged identical metal spheres are connected by an insulating spring (unstretched length 0.75 m,spring constant k=35.0 N/m).Charge +2q is placed on the first sphere and -q on the second sphere,causing the spring to contract to a length of 0.54 m.Recall that the force exerted by a spring is k $\Delta$ x,where $\Delta$ x is the change in the spring's length from its unstretched/uncompressed length.Determine the charge q.

A)1.19 * 10^-10 C
B)1.09 * 10^-5 C
C)2.06 * 10^-5 C
D)1.75 * 10^-5 C
E)3.62 * 10^-5 C

Question 6

The force between a 3.0 µC and a 2.0 µC charge is 10 N.What is the separation distance between the two charges?

A)5.2 cm
B)7.3 cm
C)8.6 cm
D)9.5 cm

Question 7

In the opposite corners of a square there are two identical ions.Each has a charge of -e.The length of one side of he square is L.In one of the other corners there is a third ion which has a charge of +e.What is the magnitude of the net electrostatic force on the positive ion caused by the two negative ions?

A)ke²/2L²
B)ke²/L²
C) ke²/L²
D)2ke²/L²

Question 8

Three electrons are located at the vertices of an equilateral triangle,one at each vertex.The length of one side of the triangle is 1.00 nm.What is the magnitude of the initial acceleration of each electron?

A)2.52 * 10²⁰ m/s²
B)3.57 * 10²⁰ m/s²
C)4.38 * 10²⁰ m/s²
D)5.05 * 10²⁰ m/s²

Question 9

Three electrons are located at the vertices of an equilateral triangle,one at each vertex.The length of one side of the triangle is 1.00 nm.What is the magnitude of the net electrostatic force on each electron?

A)2.30 * 10^-10 N
B)3.25 * 10^-10 N
C)3.99 * 10^-10 N
D)4.60 * 10^-10 N

Question 10

Two point charges are placed on two of the corners of a triangle as shown.What magnitude of force would be felt by a 1.0 µC charge placed at the right angle?

A)1.4 N
B)2.9 N
C)3.3 N
D)5.4 N
E)6.8 N

Question 11

Identical point charges Q are placed at each of the four corners of a 1.0 m * 2.0 m rectangle.If Q = 35 µC,what is the magnitude of the electrostatic force on any one of the charges?

A)12 N
B)13 N
C)14 N
D)15 N
E)16 N

Question 12

Three point charges are positioned on the x axis.If the charges and corresponding positions are -25.0 µC at x = 0.00 cm,-50.0 µC at x = 30.0 cm,and +100.0 µC at x = 80.0 cm,what is the magnitude of the electrostatic force on the -25.0 -µC charge?

A)89.7 N
B)160 N
C)8.97 mN
D)16.0 mN
E)0 N

Question 13

A particle (charge = -15.0 µC)is located on the x- axis at the point x = -25.0 cm,and a second particle (charge = +45.0 µC)is placed on the x- axis at x = +30.0 cm.What is the magnitude of the total electrostatic force on a third particle (charge = -3.50 µC)placed at the origin (x = 0)?

A)2.33 mN
B)23.3 N
C)0.818 N
D)8.18 N
E)2.67 N

Question 14

What is the total charge on 3.72 * 10¹⁹ electrons?

A)5.00 C
B)6.78 C
C)5.95 C
D)0.430 C
E)2.33 C

Question 15

Identical point charges Q are placed at each of the four corners of square 2.0 m in side.The magnitude of the electrostatic force on any one of the charges is 4.41 N.The absolute value of the charge Q is

A)32 µC.
B)15 µC.
C)48 µC.
D)23 µC.
E)67 µC.

Question 16

When two charges are separated by a distance d,the magnitude of the electrostatic force between them is F. What would be the magnitude of the electrostatic force between them if the separation distance was d/2?

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

Question 17

Two point charges are placed on two of the corners of a triangle as shown.What is the direction of the force would be felt by a 6.0 µC charge placed at the right angle relative to the horizontal (positive x-axis to the right)?

A)-18 ^$\circ$
B)+18 ^$\circ$
C)-45 ^$\circ$
D)+45 ^$\circ$
E)-85 ^$\circ$

Question 18

A charge Q₁ = Q is positioned on the x axis at x = a.Where should a charge Q₂ = 9Q be placed to produce a net electric force of zero on a charge placed at the origin?

A)at x = 2a
B)at x = -2a
C)at x = 3a
D)at x = -3a
E)at x = 4a

Question 19

A 3.0 µC charge lies 10.0 cm to the right of a 2.0 µC on the x-axis.What is the magnitude of the force on the 2.0 µC charge?

A)2.4 N
B)4.8 N
C)5.4 N
D)6.7 N
E)7.9 N

Question 20

Two point charges are fixed in space along the x-axis.The first charge of 3.8 $\mu$ C is located at x = - 4.5 cm,while the second charge of -5.6 $\mu$ C is located at x = 3.5 cm.Where should a third charge (with charge 1 $\mu$ C)be placed on the x-axis so that the total electric force it vanishes?

A)-0.214 m
B)0.214 m
C)-0.312 m
D)-0.419 m
E)0.419 m

Question 21

If you wish to lose weight,you may rub a balloon on your head.If you charge the balloon to a charge of q = -1.23µC,how much weight did you lose? The mass of an electron is 9.11 *10^-31 kg.

A)7.27 * 10^-24 N
B)6.87 * 10^-17 N
C)7.54 * 10^-16 N
D)1.21 * 10^-15 N
E)1.28 * 10^-12 N

Question 22

Two equal masses of charge 36 nC each are suspended at the end of two 1-m strings of negligible mass.The ropes make and angle of 5 ^$\circ$ with respect to each other.What is the mass of one of the two equal masses?

A)8.1 g
B)15 g
C)4.1 g
D)3.6 g
E)6.7 g

Question 23

Two small,charged objects,Q1 and Q2,are some distance d apart from each other and there is a force F between them.What is the value of the force if Q1 is increased by a factor of two,Q2 is increased by a factor of 3,and d is increased by a factor of 5?

A)0.20 F
B)0.24 F
C)0.12 F
D)1.2 F

Question 24

Two equal masses of charge 36 nC each are suspended at the end of two 1-m strings of negligible mass.The ropes make and angle of 5 ^$\circ$ with respect to each other.What is the tension in one of the strings?

A)0.060 N
B)0.044 N
C)0.019 N
D)0.023 N
E)0.035 N

Question 25

What is the net charge of 1 mole (6.02 * 10²³)of electrons?

A)-5.48 * 10^-7 C
B)5.48 * 10^-7 C
C)-6.02 * 10³ C
D)-9.63 * 10⁴ C
E)9.63 * 10⁴ C

Question 26

Find the magnitude and direction of the electrostatic force on the electron in the figure shown.

A)5.07 *10^-26 N to the left
B)5.07 * 10^-26 N to the right
C)0 N
D)6.23 * 10^-26 N to the left
E)6.23 * 10^-26 N to the right

Question 27

According to the Bohr model of the atom,an electron orbits the nucleus in a circular orbit.Find the acceleration of an electron in a circular orbit around a proton.Ignore any relativistic or quantum effects. Mass of the electron: 9.11 * 10^-31 kg
Mass of the proton: 1.67 * 10^-27 kg
Radius of orbit: 5.29* 10^-11 m

A)2.19 * 10⁶ m/s²
B)1.20 * 10⁸ m/s²
C)4.78 * 10¹² m/s²
D)4.90 * 10¹⁹ m/s²
E)9.04 * 10²² m/s²

Question 28

Find the net force between two positively charged objects,each with charge of 1.2 mC,separated by a distance of 2.0m.They are in a material where the electric permittivity is .

A)2300 N
B)3200 N
C)4600 N
D)6400 N
E)2.6 * 10¹⁴ N

Question 29

Two charges of 0.5 C are placed at (0,1)and (1,0).A charge of -0.5 C is placed at (0,0).What is the direction of the force on a positive charge placed at (1,1)?

A)towards the origin
B)towards (1,0)
C)towards (0,1)
D)away from the origin
E)There is not enough information given to tell.

Question 30

Find the magnitude of the net force on a 1.20 mC charge at the origin if there is a +2.40 mC charge at (3.0m,0)and a -5.70 mC charge at (0,4.0m).

A)1.8 kN
B)2.9 kN
C)3.8 kN
D)4.8 kN
E)16 kN

Question 31

Which of the following have a largest net force?

A)A 1-C charge a distance of 1 m from a -2-C charge.
B)A 1-C charge a distance of 0.5 m from a -1-C charge.
C)A 1-C charge exactly halfway between a -1-C charge and a 1-C charge separated by 2 m.
D)A 1-C charge exactly halfway between two -2-C charges separated by 2 m.
E)A 1-C charge a distance of 2m from a -4-C charge.

Question 32

Two equal charges of mass 15 g each are suspended at the end of two 1-m strings of negligible mass.The ropes make and angle of 5 ^$\circ$ with respect to each other.What is the charge on each?

A)36 nC
B)30 nC
C)74 nC
D)55 nC
E)64 nC

Question 33

A 1-C charge is placed at the origin with a 2-C charge placed at the coordinates (2,0).Where should a charge of -4 C be placed such that the net force on that charge is zero?

A)at x < 0
B)at 0 < x <1
C)at 1 < x <2
D)at x > 2
E)at x = 0

Question 34

Two initially uncharged identical metal spheres 1 and 2 are connected by an insulating spring (unstretched length of 0.68 m).Charge +6.2 $\mu$ C is placed on the first sphere and -6.2 $\mu$ C on the second sphere,causing the spring to contract to a length of 0.43 m.If someone coats the spring with metal to make it conducting,what is the new length of the spring? Recall that the force exerted by a spring is k $\Delta$ x,where $\Delta$ x is the change in the spring's length from its unstretched/uncompressed length.

A)0.25 m
B)0.43 m
C)0.56 m
D)0.68 m
E)0.75 m

Question 35

Two initially uncharged identical metal spheres are connected by an insulating spring (unstretched length 0.75 m).Charge +2q is placed on the first sphere and -q on the second sphere,causing the spring to contract to a length of 0.54 m.Recall that the force exerted by a spring is k $\Delta$ x,where $\Delta$ x is the change in the spring's length from its unstretched/uncompressed length and k is the spring constant.If the charge q = 2.06 * 10^-5 C,what is the spring constant?

A)125 N/m
B)187 N/m
C)35.0 N/m
D)58.3 N/m
E)142 N/m

Question 36

According to the Bohr model of the atom,an electron orbits the nucleus in a circular orbit.Find the linear speed of an electron in a circular orbit around a proton.Ignore any relativistic or quantum effects. Mass of the electron: 9.11 * 10^-31 kg
Mass of the proton: 1.67 *10^-27 kg
Radius of orbit: 5.29 *10^-11 m

A)5.6 *¹⁶ rad/s
B)3.2 * 10¹⁶ rad/s
C)7.9 * 10¹⁶ rad/s
D)4.1 * 10¹⁶ rad/s
E)1.0 * 10¹⁶ rad/s

Question 37

Two charges are placed at the corners of an equilateral triangle that is 0.25 m on each side.The first charge is 4.5 $\mu$ C and the second is 3.2 $\mu$ C.If a charge if 2.5 $\mu$ C is placed at the third corner of the triangle,what is the magnitude of the electric force on the third charge due to the first two charges?

A)0.602 N
B)1.96 N
C)2.41 N
D)3.19 N
E)4.31 N

Question 38

For a hydrogen atom of radius 10^-10 m how does the ratio of the gravitational force between the electron and the proton to the electrostatic force F_g/F_e change if the atomic radius is doubled?

A)The ratio decreases by a factor of four.
B)The ratio decreases by a factor of two.
C)The ratio remains unchanged.
D)The ratio doubles.
E)The ratio increases by a factor of four.

Question 39

Which of the following have a smallest net force?

A)A 1-C charge a distance of 1 m from a -2-C charge.
B)A 1-C charge a distance of 0.5 m from a -1-C charge.
C)A 1-C charge exactly halfway between a -1-C charge and a 1-C charge separated by 2 m.
D)A 1-C charge exactly halfway between two -2-C charges separated by 2 m.
E)A 1-C charge a distance of 2m from a -4-C charge.

Question 40

According to the Bohr model of the atom,an electron orbits the nucleus in a circular orbit.Find the linear speed of an electron in a circular orbit around a proton.Ignore any relativistic or quantum effects. Mass of the electron: 9.11 * 10^-31 kg
Mass of the proton: 1.67 *10^-27 kg
Radius of orbit: 5.29 * 10^-11 m

A)2.2 * 10⁶ m/s
B)5.6 * 10⁵ m/s
C)4.3 * 10⁶ m/s
D)5.9 * 10⁵ m/s
E)9.0 * 10⁵ m/s

Question 41

In the figure the net electrostatic force on charge Q_A is zero.If Q_A = +1 nC,determine the magnitude of Q₀ if position of Q_A is (+2a,-2a).

A)4.24 nC
B)3.04 nC
C)6.80 nC
D)9.61 nC
E)2.15 nC

Question 42

A small ball with a mass of 40 g and a charge of 0.3 $\mu$ C is suspended from the ceiling on a string.The ball is suspended a distance of 7.0 cm above an insulating floor.If a second small ball with a mass of 50 g and a charge of 0.6 $\mu$ C is placed on the floor directly beneath the first ball,what is the tension in the string?

A)0.04 N
B)0.06 N
C)0.33 N
D)0.39 N
E)0.72 N

Question 43

A plastic ball of charge -5 nC is held 2 cm above a glass bead of charge +5 nC at rest on a table.For the glass bead to leap up to the plastic ball its mass must be

A)57 $\mu$ g.
B)65 $\mu$ g.
C)81 $\mu$ g.
D)98 $\mu$ g.
E)112 $\mu$ g.

Question 44

An uncharged metal plate (P)is connected by a conductor to ground through a switch (S).The switch (S)is initially closed.A negative charge -Q is brought close to P without touching it and then the switch (S)is opened.After the switch (S)is open,the negative charge -Q is removed.After the negative charge -Q is removed,what is the charge on the plate (P)?

A)It is now positively charged.
B)It is now negatively charged.
C)It is still uncharged.
D)It cannot be determined without knowing how much charge was on the metal plate P before switch S was closed.

Question 45

A small ball with a mass of 40 g and a charge of -0.3 $\mu$ C is suspended from the ceiling on a string.The ball is suspended a distance of 7.0 cm above an insulating floor.If a second small ball with a mass of 50 g and a charge of 0.6 $\mu$ C is placed on the floor directly beneath the first ball,what is the tension in the string?

A)0.04 N
B)0.06 N
C)0.33 N
D)0.39 N
E)0.72 N

Question 46

A small ball with a mass of 40 g and a charge of -0.3 $\mu$ C is suspended from the ceiling on a string.The ball is suspended above an insulating floor.If a second small ball with a mass of 50 g and a charge of 0.6 $\mu$ C is placed on the floor directly beneath the first ball and the tension in the string is 1.0 N,what is the distance between the first ball and the insulating floor?

A)8.3 cm
B)7.0 cm
C)5.2 cm
D)5.7 cm
E)6.4 cm

Question 47

A fixed +2.0 mC charge is located at the origin,and a fixed -5.0 mC charge is located at x = 1.0 m.Where could a +7.0 mC charge be placed so that the net force on it is zero?

A)-1.7 m
B)-0.67 m
C)-0.39 m
D)+0.39 m
E)+0.67 m

Question 48

A glass rod is charged by triboelectric charging and 13 * 10¹⁰ electrons removed.What is the charge on the rod?

A)+ 6.40 nC
B)-6.40 nC
C)+20.8 nC
D)-20.8 nC
E)+8.12 nC

Question 49

A small charged ball with a mass of 40 g is suspended from the ceiling on a string.The ball is suspended a distance of 7.0 cm above an insulating floor.If a second small ball with a mass of 50 g and a charge of -0.60 $\mu$ C is placed on the floor directly beneath the first ball and the tension in the string is 1.00 N,what is the charge on the ball attached to the string?

A)0.96 $\mu$ C
B)0.55 $\mu$ C
C)0.72 $\mu$ C
D)1.3 $\mu$ C
E)0.30 $\mu$ C

Question 50

Consider two protons placed near one another with no other objects close by.They would

A)accelerate away from each other.
B)remain motionless.
C)accelerate toward each other.
D)be pulled together at constant speed.
E)move away from each other at constant speed.

Question 51

When a positively charged rod is brought near to an isolated neutral conductor without touching it,will the rod experience an attractive force,a repulsive force,or no force at all?

A)an attractive force
B)a repulsive force
C)no force at all

Question 52

In Bohr's model of the hydrogen atom an electron revolves in a circular orbit of radius 0.053 nm around a proton.The number of revolutions made by the electron in one second is

A)12.8 * 10³⁹.
B)9.8 * 10³⁵.
C)4.3 * 10³¹.
D)6.6 * 10¹⁵.
E)6.2 * 10¹².

Question 53

Two spheres carry electric charge,and a third charged sphere is now placed somewhere on the line that runs through the two spheres' centers.If the result of the placement of the third charge is that there is no net electrostatic force on each of the two original spheres,what can be said?

A)The original spheres carried charges of opposite sign.
B)The original spheres carried charges of the same sign.
C)The original spheres carried charges of equal magnitude.
D)The new charge is placed equidistant from each of the two original charges.
E)None of the choices may be said with certainty.

Question 54

Two spheres carry electric charge,and a third charged sphere is now placed between the two charged spheres on a line connecting the two spheres' centers.If the result of the placement of the third charge is that there is no net electrostatic force on each of the two original spheres,what can be said?

A)The original spheres carried charges of opposite sign.
B)The original spheres carried charges of the same sign.
C)The original spheres carried charges of equal magnitude.
D)The new charge is placed equidistant from each of the two original charges.
E)None of the choices may be said with certainty.

Question 55

What fraction of the electrons would you have to remove from a 10.0 mg sphere of iron (Z=26,A=56)in order to make its charge 1.00 C?

A)0.224%
B)0.482%
C)2.24 * 10^-4
D)4.82 * 10^-4
E)4.00 * 10^-7

Question 56

A glass rod is charged to + 6.4 nC by triboelectric charging.The number of electrons that have been removed are

A)10 * 10¹⁰.
B)4 * 10¹⁰.
C)8 * 10¹¹.
D)13 * 10¹¹.
E)19 *10¹².

Question 57

0.482% of the electrons are removed from a sphere of iron (Z=26,A=56),resulting in a net charge of 1.00 C on the sphere.What is the mass of the iron sphere?

A)4.64 mg
B)10.0 mg
C)3.19 mg
D)3.99 mg
E)6.20 mg

Question 58

The diameter of C¹² nucleus is 2.75 * 10^-15 m.It has a charge of +6e.The magnitude of the force on a proton placed 2 * 10^-15 m from its surface is

A)121.4 N.
B)345.6 N.
C)542.1 N.
D)632.5 N.
E)980.1 N.

Question 59

Two charges,q₁ = +10 nC and q₂ = -30 nC are 20 cm apart.Where (other than infinity)can a proton be placed so as to experience no net force?

A)left of charge q₁
B)on the line joining q₁ and q₂
C)right of charge q₂
D)at a point P on the right bisector of the line joining the two charges

Question 60

0.482% of the electrons are removed from a 10.0 mg sphere of iron (Z=26,A=56),resulting in a net charge on the sphere.What is the net charge on the iron sphere?

A)2.2 C
B)1.6 C
C)1.0 C
D)10.0 C
E)1.9 C

Question 61

What acceleration,will an electron experience when it is a distance of 30 nm away from a charge of Q = -30e ? (Use the sign convention here: + for acceleration away from the charge Q,and - for acceleration towards it.)

A)-7.68 * 10^-12 m/s²
B)8.43 * 10¹⁸ m/s²
C)3.26 * 10^-7 m/s²
D)- 8.99 * 10⁹ m/s²
E)+ 8.99 * 10⁹ m/s²

Question 62

How many alpha particles are needed to produce a total charge of 2.5 * 10^-12 C? (Hint: Each alpha particle contains two protons.)

A)7.8 Million
B)1.6 * 10^-19
C)2
D)839
E)4.2 * 10¹³

Question 63

Three charges of equal magnitude Q are held in the configuration shown.If a small positive charge,q,is placed at the origin what will be the magnitude and direction of the force it experiences? (Note: Pay attention to the sign on each of the three charges.)

A) in positive y-direction
B) in negative y-direction
C) in positive x-direction
D) in negative x-direction
E)0

Question 64

Two charges of 1.6 * 10^-3 C and 6.4 * 10^-4 C are a distance of 5.1 m apart.What is the magnitude of the force (in N)acting between them?

A)354 N
B)290 N
C)120 N
D)456 N
E)35 N

Question 65

Three point charges are placed on the x-axis as shown.Assume that Q1 = 2.40 $\mu$ C,Q2 = -Q1,and Q3 = Q1.The coordinates of the point charges are x1 = -0.100 m,x2 = 0.120 m,x3 = 0.300 m.What is the force (in N)on Q2?

A)0.324
B)0.366
C)0.414
D)0.468
E)0.528

Question 66

Two charged objects are a distance 2.0 m apart.Object X has a charge 33.0 C and Object Y has 3.0 C.

A)The magnitude of electrostatic force on X is 11 times that on Y.
B)The magnitude of electrostatic force on Y is 11 times that on X.
C)The electrostatic force on X is the negative of that on Y.
D)The electrostatic force on X is the same as that on Y.

Question 67

In a hydrogen atom,the average separation between the orbiting electron and the proton is 0.53 * 10^-10 m.What is the force of the electron? Use a negative sign for attractive,positive sign for repulsive force.

A)-8.2 * 10^-8 N
B)+8.2 * 10^-8 N
C)0
D)-4.4 * 10^-3 N
E)+4.4 * 10^-3 N

Question 68

Two charged particles attract each other with a force

A)is 16 times stronger.
B)is 4 time stronger.
C)is twice as strong.
D)remains the same.
E)is 1/2 as strong.

Question 69

An electron in a hydrogen atom experiences a Coulomb force,F = 85.2 * 10^-9 N,as it goes in a circular orbit around the central proton.How far away is the electron from the proton?

A)0.052 nm
B)52 $\mu$ m
C)0.35 nm
D)35 $\mu$ m
E)27 mm

Question 70

What is the force on the -4 $\mu$ C sphere?

A)550 N,to the left
B)350 N,to the left
C)0
D)350 N,to the right
E)550 N to the right