Question 1

Two 10¢ coins (dimes)carrying identical charges are lying 2.5 m apart on a table.If each of these coins experiences an electrostatic force of magnitude 2.0 N due to the other coin,how large is the charge on each coin? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 2

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

First, we can calculate the force between the two charged spheres using the formula:

F = k(q1q2/r^2)

where F is the force, k is the Coulomb constant, q1 and q2 are the charges on the spheres, and r is the distance between the centers of the spheres. Since the spheres are accelerating away from each other, we know that the net force on each sphere is:

F = ma

where m is the mass of each sphere and a is the acceleration.

Setting these two equations equal to each other and solving for q1 and q2, we get:

q1 = q2 = (ma)(r^2)/k

Plugging in the given values, we get:

q1 = q2 = (0.001 kg)(11 m/s^2)(0.02 m)^2/(9.0 × 10^9 N · m^2/C^2)

q1 = q2 = 140 nC

Therefore, the magnitude of the charge on each sphere is 140 nC, which is option A.

Question 3

As shown in the figure,the charge Q is midway between two other charges.If 
What must be the charge q1 so that charge q2 remains stationary as Q and q1 are held in place?

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Question 4

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 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? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 5

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

Accepted Answer

The force between two point charges is given by Coulomb's law:

F = k * q1 * q2 / r^2

where k is the Coulomb constant, q1 and q2 are the charges of the two point charges, and r is the distance between them.

In this problem, we have:

q1 = 1.0 µC = 1.0 × 10^-6 C
r = 15 m
F = 1.0 µN = 1.0 × 10^-6 N

We are asked to find q2. We can rearrange Coulomb's law to solve for q2:

q2 = F * r^2 / (k * q1)

Substituting the given values, we get:

q2 = (1.0 × 10^-6 N) * (15 m)^2 / (9.0 × 10^9 N m^2/C^2 * 1.0 × 10^-6 C)

q2 = 25 × 10^-9 C = 25 nC

Therefore, the best choice is E: 25 nC.

Question 6

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 = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²,e = 1.6 × 10^-19 C,m_proton = 1.67 × 10^-27 kg,m_electron = 9.11 × 10^-31 kg)

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Question 7

Two point charges each experience a 1-N electrostatic force when they are 2 cm apart.If they are moved to a new separation of 8 cm,what is the magnitude of the electric force on each of them?

Accepted Answer

The electrostatic force between two point charges is inversely proportional to the square of the distance between them (Coulomb's Law). If the distance is increased from 2 cm to 8 cm, the distance is multiplied by 4. Therefore, the force is divided by 4^2 = 16, resulting in a force of 1/16 N.

Question 8

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

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Question 9

The zirconium nucleus contains 40 protons,and an electron is 1.0 nm from the nucleus.What is the electric force on the electron due to the nucleus? ( e = 1.60 × 10^-19 C,k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The electric force can be calculated using Coulomb's law: F = k * |q1 * q2| / r^2. Here, q1 = 40e (charge of the nucleus), q2 = -e (charge of the electron), and r = 1.0 nm = 1.0 × 10^-9 m. Substituting the values, F = 9.0 × 10^9 * |40 * 1.60 × 10^-19 * 1.60 × 10^-19| / (1.0 × 10^-9)^2 = 9.2 nN.

Question 10

A particle of charge +2q is placed at the origin and particle of charge -q is placed on the x-axis at x = 2a.Where on the x-axis can a third positive charge be placed so that the net electric force on it is zero?

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Question 11

Two tiny beads,each of mass 3.2 g,carry equal-magnitude charges.When they are placed 6.4 cm apart and released in outer space,they begin to accelerate toward each other at 538 m/s².What is the magnitude of the charge on each bead? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 12

Two tiny particles carrying like charges of the same magnitude are Apart.If the electric force on one of them is What is the magnitude of the charge on each of these particles? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 13

Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side.What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 14

A proton is located at the point (x = 1.0 nm,y = 0.0 nm)and an electron is located at the point (x=0.0nm, y= 4.0nm). Find the magnitude of the electrostatic force that each one exerts on the other.(k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²,e = 1.6 × 10^-19C)

Accepted Answer

The magnitude of the electrostatic force can be calculated using Coulomb's law: $F = k \frac{|q_1q_2|}{r^2}$, where $k = 9.0 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$, $q_1 = q_2 = 1.6 \times 10^{-19} \, \text{C}$, and $r$ is the distance between the proton and the electron. The distance $r$ can be found using the Pythagorean theorem, given the positions of the proton and electron: $r = \sqrt{(1.0 \, \text{nm})^2 + (4.0 \, \text{nm})^2} = \sqrt{1 + 16} = \sqrt{17} \, \text{nm} = \sqrt{17} \times 10^{-9} \, \text{m}$. Substituting these values into Coulomb's law gives $F = 9.0 \times 10^9 \times \frac{(1.6 \times 10^{-19})^2}{(\sqrt{17} \times 10^{-9})^2}$, which calculates to approximately $1.4 \times 10^{-11} \, \text{N}$.

Question 15

The three point charges +4.0 μC,-5.0 μC,and -9.0 μC are placed on the x-axis at the points x = 0 cm,x = 40 cm,and x = 120 cm,respectively.What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 16

Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis.The +5.00-µC particle is at x = 0.00 cm,and the other particle is at x = 100.00 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?

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Question 17

As shown in the figure,three charges are at corners of a rectangle.The charge in the bottom right corner is Q = - 90 nC,and all the other quantities are accurate to two significant figures.What is the magnitude of the net electrical force on Q due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 18

As shown in the figure,three charges are at the vertices of an equilateral triangle.The charge Q is 6.7 nC,and all the other quantities are accurate to two significant figures.What is the magnitude of the net electric force on the charge Q due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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Question 19

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

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Question 20

Three point charges are located on the x-axis at the following positions: Q₁ = +2.00 μC is at x = 1.00 m,Q₂ = +3.00 μC is at x = 0.00,and Q₃ = -5.00 μC is at x = -1.00 m.What is the magnitude of the electric force on Q2? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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Quiz 19: Electric Charges, Forces, and Fields

Two 10¢ coins (dimes) carrying identical charges are lying 2.5 m apart on a table.If each of these coins experiences an electrostatic force of magnitude 2.0 N due to the other coin,how large is the charge on each coin? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

As shown in the figure,the charge Q is midway between two other charges.If What must be the charge q1 so that charge q2 remains stationary as Q and q1 are held in place?

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

Two point charges each experience a 1-N electrostatic force when they are 2 cm apart.If they are moved to a new separation of 8 cm,what is the magnitude of the electric force on each of them?

The zirconium nucleus contains 40 protons,and an electron is 1.0 nm from the nucleus.What is the electric force on the electron due to the nucleus? ( e = 1.60 × 10^-19 C,k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A particle of charge +2q is placed at the origin and particle of charge -q is placed on the x-axis at x = 2a.Where on the x-axis can a third positive charge be placed so that the net electric force on it is zero?

Two tiny beads,each of mass 3.2 g,carry equal-magnitude charges.When they are placed 6.4 cm apart and released in outer space,they begin to accelerate toward each other at 538 m/s².What is the magnitude of the charge on each bead? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two tiny particles carrying like charges of the same magnitude are Apart.If the electric force on one of them is What is the magnitude of the charge on each of these particles? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side.What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A proton is located at the point (x = 1.0 nm,y = 0.0 nm) and an electron is located at the point (x=0.0nm, y= 4.0nm) . Find the magnitude of the electrostatic force that each one exerts on the other.(k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²,e = 1.6 × 10^-19C)

The three point charges +4.0 μC,-5.0 μC,and -9.0 μC are placed on the x-axis at the points x = 0 cm,x = 40 cm,and x = 120 cm,respectively.What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Three point charges are located on the x-axis at the following positions: Q₁ = +2.00 μC is at x = 1.00 m,Q₂ = +3.00 μC is at x = 0.00,and Q₃ = -5.00 μC is at x = -1.00 m.What is the magnitude of the electric force on Q2? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Quiz 19: Electric Charges, Forces, and Fields

Two 10¢ coins (dimes) carrying identical charges are lying 2.5 m apart on a table.If each of these coins experiences an electrostatic force of magnitude 2.0 N due to the other coin,how large is the charge on each coin? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

As shown in the figure,the charge Q is midway between two other charges.If What must be the charge q1 so that charge q2 remains stationary as Q and q1 are held in place?

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

Two point charges each experience a 1-N electrostatic force when they are 2 cm apart.If they are moved to a new separation of 8 cm,what is the magnitude of the electric force on each of them?

The zirconium nucleus contains 40 protons,and an electron is 1.0 nm from the nucleus.What is the electric force on the electron due to the nucleus? ( e = 1.60 × 10-19 C,k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A particle of charge +2q is placed at the origin and particle of charge -q is placed on the x-axis at x = 2a.Where on the x-axis can a third positive charge be placed so that the net electric force on it is zero?

Two tiny beads,each of mass 3.2 g,carry equal-magnitude charges.When they are placed 6.4 cm apart and released in outer space,they begin to accelerate toward each other at 538 m/s2.What is the magnitude of the charge on each bead? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

Two tiny particles carrying like charges of the same magnitude are Apart.If the electric force on one of them is What is the magnitude of the charge on each of these particles? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side.What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A proton is located at the point (x = 1.0 nm,y = 0.0 nm) and an electron is located at the point (x=0.0nm, y= 4.0nm) . Find the magnitude of the electrostatic force that each one exerts on the other.(k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2,e = 1.6 × 10-19C)

The three point charges +4.0 μC,-5.0 μC,and -9.0 μC are placed on the x-axis at the points x = 0 cm,x = 40 cm,and x = 120 cm,respectively.What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

Three point charges are located on the x-axis at the following positions: Q1 = +2.00 μC is at x = 1.00 m,Q2 = +3.00 μC is at x = 0.00,and Q3 = -5.00 μC is at x = -1.00 m.What is the magnitude of the electric force on Q2? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Two 10¢ coins (dimes) carrying identical charges are lying 2.5 m apart on a table.If each of these coins experiences an electrostatic force of magnitude 2.0 N due to the other coin,how large is the charge on each coin? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart.When released,they begin to accelerate away from each other at What is the magnitude of the charge on each sphere,assuming only that the electric force is present? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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

The zirconium nucleus contains 40 protons,and an electron is 1.0 nm from the nucleus.What is the electric force on the electron due to the nucleus? ( e = 1.60 × 10^-19 C,k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two tiny beads,each of mass 3.2 g,carry equal-magnitude charges.When they are placed 6.4 cm apart and released in outer space,they begin to accelerate toward each other at 538 m/s².What is the magnitude of the charge on each bead? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two tiny particles carrying like charges of the same magnitude are Apart.If the electric force on one of them is What is the magnitude of the charge on each of these particles? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side.What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A proton is located at the point (x = 1.0 nm,y = 0.0 nm) and an electron is located at the point (x=0.0nm, y= 4.0nm) . Find the magnitude of the electrostatic force that each one exerts on the other.(k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²,e = 1.6 × 10^-19C)

The three point charges +4.0 μC,-5.0 μC,and -9.0 μC are placed on the x-axis at the points x = 0 cm,x = 40 cm,and x = 120 cm,respectively.What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Three point charges are located on the x-axis at the following positions: Q₁ = +2.00 μC is at x = 1.00 m,Q₂ = +3.00 μC is at x = 0.00,and Q₃ = -5.00 μC is at x = -1.00 m.What is the magnitude of the electric force on Q2? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)