Question 1

The figure shows three electric charges labeled Q₁,Q₂,Q₃,and some electric field lines in the region surrounding the charges.What are the signs of the three charges?

Accepted Answer

From the electric field lines, we can see that the charges Q₁ and Q₃ are positive because the field lines originate from them and diverge outward. The charge Q₂ is negative because the field lines converge toward it. Therefore, the correct choice is A.

Question 2

Charge Q₁ = 6.0 nC is at (0.30 m,0),charge Q₂ = -1.0 nC is at (0,0.10 m),and charge .What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε₀ =

Accepted Answer

5.4 × 10^-6 N,56° above -x-axis

Question 3

One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the distance between the balls in the test tube would become

Accepted Answer

The force between two charges q1 and q2 separated by a distance d is given by Coulomb's law:

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

where k is the Coulomb constant.

When we double the charge on both balls, the force between them becomes:

F' = k * (2q1 * 2q2) / d^2 = 4 * (k * (q1 * q2) / d^2) = 4F

According to Newton's second law, F = mg, where m is the mass of each ball and g is the gravitational acceleration. Since the balls are in equilibrium, the gravitational force on each ball is balanced by the electrostatic force from the other ball:

mg = F

When we double the charge on both balls, the electrostatic force becomes 4F, so in order to balance it, the distance between the balls needs to increase by a factor of 2:

mg = 4F'

mg = 4 * (k * (q1 * q2) / d^2)

d' = sqrt(4 * d^2) = 2d

Therefore, the answer is B) 2d.

Question 4

X and Y are two uncharged metal spheres on insulating stands,and are in contact with each other.A positively charged rod R is brought close to X as shown in Figure (a).  Sphere Y is now moved away from X,as in Figure (b).  What are the final charge states of X and Y?

Accepted Answer

The answer of X and Y are two uncharged metal...

Question 5

Two very large parallel sheets a distance d apart have their centers directly opposite each other.The sheets carry equal but opposite uniform surface charge densities.A point charge that is placed near the middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets.If this charge is now moved closer to one of the sheets so that it is a distance d/4 from that sheet,what force will feel?

Accepted Answer

The electric field between two parallel plates with equal but opposite charge is uniform. This means the force experienced by a point charge in this field does not depend on its position between the plates. Therefore, even when the charge is moved closer to one of the sheets, the force it feels remains F.

Question 6

A positive point charge Q is fixed on a very large horizontal frictionless tabletop.A second positive point charge q is released from rest near the stationary charge and is free to move.Which statement best describes the motion of q after it is released?

Accepted Answer

As the charge q moves away from the fixed charge Q, the repulsive force decreases, but q continues to accelerate due to the initial force, causing its speed to keep increasing.

Question 7

The figure shows two unequal point charges,q and Q,of opposite sign.Charge Q has greater magnitude than charge q.In which of the regions X,Y,Z will there be a point at which the net electric field due to these two charges is zero?

Accepted Answer

The answer of The figure shows two unequal point charges,q...

Question 8

A point charge Q is located a short distance from a point charge 3Q,and no other charges are present.If the electrical force on Q is F,what is the electrical force on 3Q?

Accepted Answer

The answer of A point charge Q is located a...

Question 9

A piece of plastic has a net charge of +2.00 μC.How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10^-19 C)

Accepted Answer

The net charge is +2.00 μC, which means there are more protons than electrons. The charge of one proton is 1.60 × 10^-19 C. To find the number of excess protons, divide the net charge by the charge of one proton: (2.00 × 10^-6 C) / (1.60 × 10^-19 C/proton) = 1.25 × 10^13 protons.

Question 10

Two identical small charged spheres are a certain distance apart,and each one initially experiences an electrostatic force of magnitude F due to the other.With time,charge gradually leaks off of both spheres.When each of the spheres has lost half its initial charge,the magnitude of the electrostatic force will be

Accepted Answer

The electrostatic force between two charged spheres is given by Coulomb's law:

F = kq1q2/r^2

where k is the Coulomb constant, q1 and q2 are the charges on the spheres, and r is the distance between them.

If each sphere loses half its initial charge, the new charges on the spheres will be q1/2 and q2/2, respectively. The distance between them, however, remains the same.

Using the new charges in Coulomb's law, the new electrostatic force between the spheres is:

F' = k(q1/2)(q2/2)/r^2 = kq1q2/4r^2 = F/4

Thus, when each sphere has lost half its initial charge, the magnitude of the electrostatic force between them will be 1/4 of the initial force.

Therefore, the best choice is C) 1/4 F.

Question 11

An electron is initially moving to the right when it enters a uniform electric field directed upwards.Which trajectory shown below will the electron follow?

Accepted Answer

The answer of An electron is initially moving to the...

Question 12

Three point charges are placed on the x-axis.A charge of +2.0 μC is placed at the origin,-2.0 μC to the right at x = 50 cm,and +4.0 μC at the 100 cm mark.What are the magnitude and direction of the electrostatic force that acts on the charge at the origin? (k = 1/4πε₀ =

Accepted Answer

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

Question 13

Two point charges Q₁ and Q₂ of equal magnitudes and opposite signs are positioned as shown in the figure.Which of the arrows best represents the net electric field at point P due to these two charges?

Accepted Answer

The answer of Two point charges Q₁ and Q₂ of...

Question 14

Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure.Which of the arrows represents the direction of the net electric field at the center of the square?

Accepted Answer

The answer of Three equal negative point charges are placed...

Question 15

When two point charges are a distance d part,the electric force that each one feels from the other has magnitude F.In order to make this force twice as strong,the distance would have to be changed to

Accepted Answer

The answer of When two point charges are a distance...

Question 16

Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1),(-1,1),(-1,-1),(1,-1).The electric field on the x-axis at (1,0)points in the same direction as

Accepted Answer

The answer of Four equal negative point charges are located...

Question 17

Two large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

Accepted Answer

The electric field between two parallel plates is given by $E = \frac{\sigma}{\varepsilon_0}$, where $\sigma$ is the surface charge density and $\varepsilon_0$ is the permittivity of free space. This formula shows that the electric field is independent of the distance between the plates, so halving the distance does not change the magnitude of the electric field.

Question 18

Two identical small conducting spheres are separated by 0.60 m.The spheres carry different amounts of charge and each sphere experiences an attractive electric force of 10.8N.The total charge on the two spheres is -24 μC.The two spheres are now connected by a slender conducting wire,which is then removed.The electric force on each sphere is closest to

Accepted Answer

The answer of Two identical small conducting spheres are separated...

Question 19

When two point charges are 2.0 cm apart,each one experiences a 1.0-N electric force due to the other charge.If they are moved to a new separation of 8.0 cm,the electric force on each of them is closest to

Accepted Answer

The electric force between two point charges is inversely proportional to the square of the distance between them (Coulomb's Law). When the distance is increased from 2.0 cm to 8.0 cm (a factor of 4), the force is reduced by a factor of $4^2 = 16$. Therefore, the new force is $1.0 \, \text{N} / 16 = 0.0625 \, \text{N}$, which is closest to 0.063 N.

Question 20

A 1.0-C point charge is 15 m from a second point charge,and the electric force on one of them due to the other is 1.0 N.What is the magnitude of the second charge?

Accepted Answer

Using Coulomb's Law, we have:

F = k(Q1*Q2)/r^2

where k is the Coulomb constant, Q1 is the charge of one point charge, Q2 is the charge of the other point charge, and r is the distance between them.

Plugging in the given values, we get:

1.0 N = (9.0 x 10^9 Nm^2/C^2) * (1.0 C) * Q2 / (15 m)^2

Solving for Q2, we get:

Q2 = (1.0 N * (15 m)^2) / (9.0 x 10^9 Nm^2/C^2) = 25 nC

Therefore, the answer is E) 25 nC.

Quiz 21: Electric Charge and Electric Field

The figure shows three electric charges labeled Q₁,Q₂,Q₃,and some electric field lines in the region surrounding the charges.What are the signs of the three charges?

Charge Q₁ = 6.0 nC is at (0.30 m,0),charge Q₂ = -1.0 nC is at (0,0.10 m),and charge .What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε₀ =

One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the distance between the balls in the test tube would become

X and Y are two uncharged metal spheres on insulating stands,and are in contact with each other.A positively charged rod R is brought close to X as shown in Figure (a) . Sphere Y is now moved away from X,as in Figure (b) . What are the final charge states of X and Y?

A positive point charge Q is fixed on a very large horizontal frictionless tabletop.A second positive point charge q is released from rest near the stationary charge and is free to move.Which statement best describes the motion of q after it is released?

The figure shows two unequal point charges,q and Q,of opposite sign.Charge Q has greater magnitude than charge q.In which of the regions X,Y,Z will there be a point at which the net electric field due to these two charges is zero?

A point charge Q is located a short distance from a point charge 3Q,and no other charges are present.If the electrical force on Q is F,what is the electrical force on 3Q?

A piece of plastic has a net charge of +2.00 μC.How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10^-19 C)

An electron is initially moving to the right when it enters a uniform electric field directed upwards.Which trajectory shown below will the electron follow?

Three point charges are placed on the x-axis.A charge of +2.0 μC is placed at the origin,-2.0 μC to the right at x = 50 cm,and +4.0 μC at the 100 cm mark.What are the magnitude and direction of the electrostatic force that acts on the charge at the origin? (k = 1/4πε₀ =

Two point charges Q₁ and Q₂ of equal magnitudes and opposite signs are positioned as shown in the figure.Which of the arrows best represents the net electric field at point P due to these two charges?

Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure.Which of the arrows represents the direction of the net electric field at the center of the square?

When two point charges are a distance d part,the electric force that each one feels from the other has magnitude F.In order to make this force twice as strong,the distance would have to be changed to

Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as

Two large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

When two point charges are 2.0 cm apart,each one experiences a 1.0-N electric force due to the other charge.If they are moved to a new separation of 8.0 cm,the electric force on each of them is closest to

A 1.0-C point charge is 15 m from a second point charge,and the electric force on one of them due to the other is 1.0 N.What is the magnitude of the second charge?

Quiz 21: Electric Charge and Electric Field

The figure shows three electric charges labeled Q1,Q2,Q3,and some electric field lines in the region surrounding the charges.What are the signs of the three charges?

Charge Q1 = 6.0 nC is at (0.30 m,0),charge Q2 = -1.0 nC is at (0,0.10 m),and charge .What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε0 =

One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure.The balls are in equilibrium a distance d apart.If the charge on each ball is doubled,the distance between the balls in the test tube would become

X and Y are two uncharged metal spheres on insulating stands,and are in contact with each other.A positively charged rod R is brought close to X as shown in Figure (a) . Sphere Y is now moved away from X,as in Figure (b) . What are the final charge states of X and Y?

A positive point charge Q is fixed on a very large horizontal frictionless tabletop.A second positive point charge q is released from rest near the stationary charge and is free to move.Which statement best describes the motion of q after it is released?

The figure shows two unequal point charges,q and Q,of opposite sign.Charge Q has greater magnitude than charge q.In which of the regions X,Y,Z will there be a point at which the net electric field due to these two charges is zero?

A point charge Q is located a short distance from a point charge 3Q,and no other charges are present.If the electrical force on Q is F,what is the electrical force on 3Q?

A piece of plastic has a net charge of +2.00 μC.How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10-19 C)

An electron is initially moving to the right when it enters a uniform electric field directed upwards.Which trajectory shown below will the electron follow?

Three point charges are placed on the x-axis.A charge of +2.0 μC is placed at the origin,-2.0 μC to the right at x = 50 cm,and +4.0 μC at the 100 cm mark.What are the magnitude and direction of the electrostatic force that acts on the charge at the origin? (k = 1/4πε0 =

Two point charges Q1 and Q2 of equal magnitudes and opposite signs are positioned as shown in the figure.Which of the arrows best represents the net electric field at point P due to these two charges?

Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure.Which of the arrows represents the direction of the net electric field at the center of the square?

When two point charges are a distance d part,the electric force that each one feels from the other has magnitude F.In order to make this force twice as strong,the distance would have to be changed to

Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1) ,(-1,1) ,(-1,-1) ,(1,-1) .The electric field on the x-axis at (1,0) points in the same direction as

Two large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

When two point charges are 2.0 cm apart,each one experiences a 1.0-N electric force due to the other charge.If they are moved to a new separation of 8.0 cm,the electric force on each of them is closest to

A 1.0-C point charge is 15 m from a second point charge,and the electric force on one of them due to the other is 1.0 N.What is the magnitude of the second charge?

The figure shows three electric charges labeled Q₁,Q₂,Q₃,and some electric field lines in the region surrounding the charges.What are the signs of the three charges?

Charge Q₁ = 6.0 nC is at (0.30 m,0),charge Q₂ = -1.0 nC is at (0,0.10 m),and charge .What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε₀ =

A piece of plastic has a net charge of +2.00 μC.How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10^-19 C)

Three point charges are placed on the x-axis.A charge of +2.0 μC is placed at the origin,-2.0 μC to the right at x = 50 cm,and +4.0 μC at the 100 cm mark.What are the magnitude and direction of the electrostatic force that acts on the charge at the origin? (k = 1/4πε₀ =

Two point charges Q₁ and Q₂ of equal magnitudes and opposite signs are positioned as shown in the figure.Which of the arrows best represents the net electric field at point P due to these two charges?