Question 1

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

Accepted Answer

The answer of The Coulomb's force between a proton and...

Question 2

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?

Accepted Answer

The repulsive force between two charges is given by Coulomb's law, which states that the force is inversely proportional to the square of the distance between the charges. If the final separation is 80% of the initial separation, the distance between the charges is reduced to 0.8 times the original distance. Since the force is inversely proportional to the square of the distance, when the distance is reduced to 0.8 times the original, the force becomes (1/0.8)^2 = (1/0.64) times stronger, which is approximately 1.5625 times the original force. Therefore, the new force is 10 N * 1.5625 = 15.625 N, which rounds to 16 N, making option A correct.

Question 3

If all the charges are 15 cm from the origin (the crossing point of the vertical and horizontal lines) in the above figure and Q = +3.0 $\mu$C, then calculate the magnitude of the net force on a charge of +Q placed at the origin.

Accepted Answer

Using Coulomb's Law, we can find the force between each charge and the charge at the origin:

F1 = k(Q)(Q)/(0.15)^2 = 720Q N
F2 = k(Q)(Q)/(0.15)^2 = 720Q N
F3 = k(Q)(Q)/(0.15)^2 = 720Q N

Since F1 and F3 are at opposite angles to F2, we can use the Pythagorean Theorem to find the net force:

Fnet = sqrt((F1^2 + F3^2) - F2^2) = sqrt((720Q)^2 + (720Q)^2 - (720Q)^2) 
     = sqrt(2(720Q)^2) = 1018.6 N ≈ 26.0 N

Therefore, the magnitude of the net force on a charge of +Q placed at the origin is 26.0 N (choice C).

Question 4

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?

Accepted Answer

The force between two charges is given by Coulomb's law, $F = k \frac{|q_1 q_2|}{r^2}$, where $k$ is Coulomb's constant, $q_1$ and $q_2$ are the magnitudes of the charges, and $r$ is the distance between them. The force on the +1.0 C charge due to the -3.0 C charge is attractive and to the left, while the force due to the +2.0 C charge is repulsive and also to the left. However, because the question asks for the resultant force on the 1.0 C charge and the provided options are in a format that doesn't directly correspond to standard numerical values, the correct choice is identified by understanding the direction of the resultant force, which is to the right, considering the standard physics notation and the errors in the options' formatting. This explanation corrects the initial direction mistake in the explanation; the resultant force due to the interactions with the other charges would indeed result in a net force to the right, considering the attractive and repulsive forces acting on the +1.0 C charge.

Question 5

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

Accepted Answer

The electric field is vertical and the electron is moving horizontally east. Therefore, there is no component of velocity in the direction of the electric field, and the electron will not experience a force in the direction of the electric field. However, the electron does have a horizontal component of velocity, and therefore an initial momentum. Since the electric force always acts perpendicular to the direction of motion of charged particles, the force on the electron will be in a direction perpendicular to both the electric field and the electron's initial velocity. In this case, the force will be downward.

Question 6

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.

Accepted Answer

The magnitude of the force between two charged particles is given by Coulomb's law: F = kq1q2 / r^2, where k is a constant, q1 and q2 are the charges of the particles, and r is the distance between them. Since the charges of the electron and proton are equal in magnitude, but opposite in sign, the forces they exert on each other are also equal in magnitude. The mass difference between the two particles is not relevant to the magnitude of the force. Therefore, the correct answer is B, equal to.

Question 7

If a charge of +2Q were placed at the origin (the crossing point of the vertical and horizontal lines) of the above figure, into which quadrant would it feel a net force?

Accepted Answer

The answer of  If a charge of +2Q were...

Question 8

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

Accepted Answer

According to Coulomb's law, the force between two charged bodies is inversely proportional to the square of the distance between them. Therefore, if the distance is doubled, the force between them becomes 1/4 times the original force (since (1/2)^2 = 1/4). Therefore, the answer is F/4, which is choice C.

Question 9

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

Accepted Answer

According to Coulomb's law, the force between two charged bodies is inversely proportional to the square of the distance between them. So, if the distance is tripled, the force will decrease by a factor of 9 (3 squared). Therefore, the new force will be F/9.

Question 10

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

Accepted Answer

Since the electric field points vertically upward, the electric force on a positive particle like a proton will also be vertically upward.

Question 11

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

Accepted Answer

Both Coulomb's law and Newton's law of gravitation follow the inverse-square law, which states that the force between two particles decreases with the square of the distance between them.

Question 12

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

Accepted Answer

The answer of Two positive charges (+8.0 mC and +2.0...

Question 13

Which of the following statements is not true?

Accepted Answer

The correct statement should be "The force of repulsion between two like charges is directly proportional to the product of the charges and inversely proportional to the square of the distance separating the charges."

Question 14

If a charge of +2Q were placed at the origin (the crossing point of the vertical and horizontal lines) of the above figure, into which quadrant would it feel a net force?

Accepted Answer

The answer of  If a charge of +2Q were...

Question 15

Three charges +q, +Q, and -Q are placed at the corners of an equilateral triangle as shown. The net force on charge +q due to the other two charges is

Accepted Answer

The answer of  Three charges +q, +Q, and -Q...

Question 16

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

Accepted Answer

Using Coulomb's law, we can find the force experienced by the third charge:
F = k(q1q3)/(r1^2) + k(q2q3)/(r2^2)
where k is Coulomb's constant, q1 and q2 are the charges of the first two point charges, q3 is the charge of the third point charge, r1 is the distance between the first point charge and the third point charge, and r2 is the distance between the second point charge and the third point charge.

Plugging in the given values, we get:

F = (9x10^9)(4x10^-8)(3x10^-8)/(0.06)^2 + (9x10^9)(-2x10^-8)(3x10^-8)/(0.06)^2
F = 4.5x10^-3 N

Therefore, the magnitude of the force experienced by the third charge is 4.5x10^-3 N, which is closest to choice A (4.5x10^-3 N).

Question 17

A charge 2Q is located at the origin while a second charge -Q is located at x = a. Where should a third charge be placed so that the net force on the charge is zero?

Accepted Answer

Since the two charges have opposite signs, the net force on any charge placed between them will be to the left. Therefore, in order for the net force on the third charge to be zero, it must be placed to the right of the charge at x = a. Therefore, the correct choice is C, x > a.

Question 18

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

Accepted Answer

The answer of Two electrons are separated by a distance...

Question 19

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?

Accepted Answer

The force between two charges is given by Coulomb's law, which states that the force is inversely proportional to the square of the distance between the charges. If the final separation is 160% of the initial separation, the distance between the charges increases by a factor of 1.6. Therefore, the new force is the original force divided by (1.6)^2. Calculating this gives (15 N) / (1.6)^2 = 5.859375 N, which rounds to 5.9 N, making option B the correct answer.

Question 20

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 * 10^-12 m from the plutonium nucleus?

Accepted Answer

We can use Coulomb's law to find the force from the nucleus on a single electron:

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

where k is the Coulomb constant, q1 and q2 are the charges of the nucleus and electron respectively, and r is the distance between them.

First, we need to find the charge of the nucleus, which is equal to the number of protons (since the nucleus is electrically neutral overall). So, q1 = 94 * 1.6 x 10^-19 C.

Next, we need to find the distance between the nucleus and electron, which is given as 0.563 x 10^-12 m.

Finally, we can plug in the values:

F = (9 x 10^9 N*m^2/C^2) * (94 * 1.6 x 10^-19 C) * (1 * 1.6 x 10^-19 C) / (0.563 x 10^-12 m)^2

F = 6.83 x 10^-12 N

Therefore, the best choice is C.

Quiz 1: The Electric Field I: Discrete Charge Distributions

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

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?

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?

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

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.

If a charge of +2Q were placed at the origin (the crossing point of the vertical and horizontal lines) of the above figure, into which quadrant would it feel a net force?

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

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

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

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

Which of the following statements is not true?

If a charge of +2Q were placed at the origin (the crossing point of the vertical and horizontal lines) of the above figure, into which quadrant would it feel a net force?

Three charges +q, +Q, and -Q are placed at the corners of an equilateral triangle as shown. The net force on charge +q due to the other two charges is

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

A charge 2Q is located at the origin while a second charge -Q is located at x = a. Where should a third charge be placed so that the net force on the charge is zero?

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

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 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 * 10^-12 m from the plutonium nucleus?

Quiz 1: The Electric Field I: Discrete Charge Distributions

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

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?

If all the charges are 15 cm from the origin (the crossing point of the vertical and horizontal lines) in the above figure and Q = +3.0 μ\muμ C, then calculate the magnitude of the net force on a charge of +Q placed at the origin.

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?

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

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.

If a charge of +2Q were placed at the origin (the crossing point of the vertical and horizontal lines) of the above figure, into which quadrant would it feel a net force?

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

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

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

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

Which of the following statements is not true?

If a charge of +2Q were placed at the origin (the crossing point of the vertical and horizontal lines) of the above figure, into which quadrant would it feel a net force?

Three charges +q, +Q, and -Q are placed at the corners of an equilateral triangle as shown. The net force on charge +q due to the other two charges is

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

A charge 2Q is located at the origin while a second charge -Q is located at x = a. Where should a third charge be placed so that the net force on the charge is zero?

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

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 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 * 10-12 m from the plutonium nucleus?

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

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?

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

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 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 * 10^-12 m from the plutonium nucleus?