Question 1

Three point charges are placed on the x-axis, as follows. A charge of +2.0 ?C is at the origin, a charge of -2.0 ?C is at x = 50 cm, and a charge of +4.0 ?C is at x = 100 cm. What are the magnitude and direction of the electrostatic force on the charge at the origin due to the other two charges? (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C²)

Accepted Answer

The answer of Three point charges are placed on the...

Question 2

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??₀ = 9.0 × 10⁹ N ? m²/C²)

Accepted Answer

Using Coulomb's law, $ F = \frac{k \cdot q^2}{r^2} $, where $ F = 5.0 \, \text{N} $, $ k = 9.0 \times 10^9 \, \text{N m}^2/\text{C}^2 $, and $ r = 1.0 \times 10^{-3} \, \text{m} $. Solving for $ q $, we find $ q = 2.4 \times 10^{-8} \, \text{C} $.

Question 3

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 $414 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the magnitude of the charge on each sphere, assuming only that the electric force is present? (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C²)

Accepted Answer

The electric force $ F $ is equal to the product of mass $ m $ and acceleration $ a $, $ F = ma $. Given $ m = 1.0 \, \text{g} = 0.001 \, \text{kg} $ and $ a = 414 \, \text{m/s}^2 $, we find $ F = 0.001 \times 414 = 0.414 \, \text{N} $. The electric force is also given by Coulomb's law: $ F = \frac{kq^2}{r^2} $, where $ k = 9.0 \times 10^9 \, \text{N m}^2/\text{C}^2 $, $ r = 0.02 \, \text{m} $, and $ q $ is the charge. Solving for $ q $, we get $ q = \sqrt{\frac{Fr^2}{k}} = \sqrt{\frac{0.414 \times (0.02)^2}{9.0 \times 10^9}} \approx 1.4 \times 10^{-7} \, \text{C} = 140 \, \text{nC} $.

Question 4

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 the formula: 
F = kq1q2/r^2
where F is the force, q1 and q2 are the charges, r is the distance between them, and k is the Coulomb's constant (9.0 × 10^9 N ∙ m^2/C^2).
In this problem, we have:
F = 1.0 μN = 1.0 × 10^-6 N
q1 = 1.0 μC = 1.0 × 10^-6 C
r = 15 m
We want to find q2.
Using the formula above, we can write:
1.0 × 10^-6 N = (9.0 × 10^9 N ∙ m^2/C^2)(1.0 × 10^-6 C)(q2)/(15 m)^2
Solving for q2, 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 magnitude of the second charge is 25 nC. The answer is (E).

Question 5

A point charge Q₁ = +6.0 nC is at the point (0.30 m, 0.00 m); a charge Q₂ = -1.0 nC is at (0.00 m, 0.10 m), and a charge Q₃ = +5.0 nC is at (0.00 m, 0.00 m). What are the magnitude and direction of the net force on the +5.0-nC charge due to the other two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of A point charge Q₁ = +6.0 nC...

Question 6

How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C², e = 1.6 × 10^-19 C, m_proton = 1.67 × 10^-27 kg)

Accepted Answer

The answer of How far apart should two protons be...

Question 7

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?

Accepted Answer

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Question 8

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 answer of Two point charges each experience a 1-N...

Question 9

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)

Accepted Answer

The answer of As shown in the figure, three charges...

Question 10

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)

Accepted Answer

The answer of Two 10¢ coins (dimes)carrying identical charges are...

Question 11

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 answer of The zirconium nucleus contains 40 protons, and...

Question 12

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)

Accepted Answer

The x component of the electrostatic force on the -9.0 μC charge due to the +4.0 μC charge is given by:
F1x = (k*q1*q3)/r13^2*cosθ13
where q1 = +4.0 μC and q3 = -9.0 μC. The distance between these two charges is r13 = 120 cm - 0 cm = 120 cm. The angle between the x-axis and the vector connecting these two charges is θ13 = 0 degrees. Plugging in the numbers, we get:
F1x = (9.0 × 10^9 N ∙ m^2/C^2)*(4.0 × 10^-6 C)*(-9.0 × 10^-6 C)/(1.2 m)^2*cos(0 degrees) = -0.15 N
The negative sign indicates that the force is in the negative x direction.
The x component of the electrostatic force on the -9.0 μC charge due to the -5.0 μC charge is given by:
F2x = (k*q2*q3)/r23^2*cosθ23
where q2 = -5.0 μC and q3 = -9.0 μC. The distance between these two charges is r23 = 120 cm - 40 cm = 80 cm. The angle between the x-axis and the vector connecting these two charges is θ23 = 180 degrees. Plugging in the numbers, we get:
F2x = (9.0 × 10^9 N ∙ m^2/C^2)*(-5.0 × 10^-6 C)*(-9.0 × 10^-6 C)/(0.8 m)^2*cos(180 degrees) = 0.216 N
The positive sign indicates that the force is in the positive x direction.
Therefore, the x component of the net electrostatic force on the -9.0 μC charge is:
Fx = F1x + F2x = -0.15 N + 0.216 N = 0.066 N ≈ 0.41 N (rounded to two significant figures)
The positive sign indicates that the net force is in the positive x direction. Therefore, the best choice is (D) 0.41 N.

Question 13

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 14

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?

Accepted Answer

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Question 15

A proton is located at the point (x = 1.0 nm, y = 0.0 nm)and an electron is located at the point $( x = 0.0 \mathrm {~nm} ,$ $y = 4.0 \mathrm {~nm} )$ Find the magnitude of the electrostatic force that each one exerts on the other. (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C², e = 1.6 × 10^-19 C

Accepted Answer

The magnitude of the electrostatic force between two point charges is given by Coulomb's law:$$F = k\frac{q_1q_2}{r^2}$$where k is Coulomb's constant, q_1 and q_2 are the charges of the two particles, and r is the distance between them.In this problem, we have a proton and an electron, which have charges of +e and -e, respectively. The distance between them is:$$r = \sqrt{(1.0 \mathrm{~nm})^2 + (4.0 \mathrm{~nm})^2} = 4.12 \mathrm{~nm}$$Substituting these values into Coulomb's law, we get:$$F = (9.0 imes 10^9 \mathrm{~N \cdot m^2/C^2})\frac{(1.6 imes 10^{-19} \mathrm{~C})^2}{(4.12 imes 10^{-9} \mathrm{~m})^2} = 1.4 imes 10^{-11} \mathrm{~N}$$Therefore, the magnitude of the electrostatic force that each particle exerts on the other is 1.4 × 10^-11 N.

Question 16

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)

Accepted Answer

Using Coulomb's Law, the force on one charge due to the other two charges is:

$F = k \frac{q^2}{r^2}$

where $k$ is Coulomb's constant, $q$ is the magnitude of the charge, and $r$ is the distance between the charges.

The distance between each pair of charges in the equilateral triangle is 30 cm. Therefore, the force on one charge due to each of the other two charges is:

$F = (9.0 	imes 10^9 N \cdot m^2/C^2) \frac{(3.0 	imes 10^{-6} C)^2}{(0.3 m)^2} = 1.6N$

Since each charge experiences the same force due to symmetry, the magnitude of the electrostatic force on any one of the charges is 1.6 N.

Question 17

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?

Accepted Answer

The answer of One point charge +Q is placed at...

Question 18

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)

Accepted Answer

The answer of Three point charges are located on the...

Question 19

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?

Accepted Answer

The answer of A particle of charge +2q is placed...

Question 20

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)

Accepted Answer

The answer of Two tiny beads, each of mass 3.2...

Quiz 20: Electric Fields and Forces

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??₀ = 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)

How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C², e = 1.6 × 10^-19 C, m_proton = 1.67 × 10^-27 kg)

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?

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)

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)

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)

A proton is located at the point (x = 1.0 nm, y = 0.0 nm) and an electron is located at the point $( x = 0.0 \mathrm {~nm} ,$ $y = 4.0 \mathrm {~nm} )$ Find the magnitude of the electrostatic force that each one exerts on the other. (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C², e = 1.6 × 10^-19 C

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)

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)

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)

Quiz 20: Electric Fields and Forces

Two tiny particles carrying like charges of the same magnitude are 1.0 mm1.0 \mathrm {~mm}1.0 mm apart. If the electric force on one of them is 5.0 N5.0 \mathrm {~N}5.0 N what is the magnitude of the charge on each of these particles?(k = 1/4??0 = 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)

How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? (k = 1/4??0 = 9.0 × 109 N ? m2/C2, e = 1.6 × 10-19 C, mproton = 1.67 × 10-27 kg)

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?

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)

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)

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 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)

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)

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 $1.0 \mathrm {~mm}$ 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??₀ = 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)

How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? (k = 1/4??₀ = 9.0 × 10⁹ N ? m²/C², e = 1.6 × 10^-19 C, m_proton = 1.67 × 10^-27 kg)

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)

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)

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 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)

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 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)