Question 1

A long, thin rod parallel to the y-axis is located at x = -1.0 cm and carries a uniform linear charge density of +1.0 nC/m. A second long, thin rod parallel to the z-axis is located at x = +1.0 cm and carries a uniform linear charge density of -1.0 nC/m. What is the net electric field due to these rods at the origin? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Accepted Answer

D

Question 2

A 3.0-μC positive point charge is located at the origin and a  positive point charge is located at   Find the coordinates of the point where the net electric field strength due to these charges is zero.

Accepted Answer

A

Question 3

Two thin 80.0-cm rods are oriented at right angles to each other. Each rod has one end at the origin of the coordinates, and one of them extends along the +x-axis while the other extends along the +y-axis. The rod along the +x-axis carries a charge of -15.0 µC distributed uniformly along its length, and the other rod carries +15.0 µC uniformly over its length. Find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm, 40.0 cm). (e = 1.60 × 10^-19 C, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Accepted Answer

1.35 × 10^-13 N at 135° with respect to the +x-axis

Question 4

A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero?

Accepted Answer

The answer of A 5.0-μC point charge is placed at...

Question 5

Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-μC charge. Find the magnitude of the electric field at the center of the square. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of Three +3.0-μC point charges are at the...

Question 6

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 7

Two point charges, Q₁= -1.0 μC and Q₂= + 4.0 μC, are placed as shown in the figure. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The y component of the electric field, at the origin O, is closest to

Accepted Answer

The answer of Two point charges, Q₁= -1.0 μC...

Question 8

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

The answer of The figure shows three electric charges labeled...

Question 9

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,...

Question 10

Three equal negative point charges are placed at three of the corners of a square of side d. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

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

Question 11

At a distance of 4.3 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Accepted Answer

The answer of At a distance of 4.3 cm from...

Question 12

A point charge Q = -500 nC and two unknown point charges, q₁ and q₂, are placed as shown in the figure. The electric field at the origin O, due to charges Q, q₁ and q₂, is equal to zero. The charge q₁ is closest to

Accepted Answer

The answer of A point charge Q = -500 nC...

Question 13

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 14

A very long wire carries a uniform linear charge density of What is the electric field strength from the center of the wire at a point on the wire's perpendicular bisector? (ε₀ = 8.85 × 10^-12 C^2/N ∙ m²)

Accepted Answer

The answer of A very long wire carries a uniform...

Question 15

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 16

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 17

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 18

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the magnitude of electric field due to these charges at a point midway between them? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of Two point charges of +20.0 μC and...

Question 19

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 20

A thin, circular disk of radius 30.0 cm is oriented in the yz-plane with its center at the origin. The disk carries a total charge of +3.00 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15.0 cm along the x-axis. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Accepted Answer

The electric field due to a uniformly charged disk at a point along its axis can be calculated using the formula derived from integrating Coulomb's law over the disk's surface. The formula for the electric field $E$ at a distance $x$ from the center of the disk along its axis is given by:$$E = \frac{\sigma}{2\epsilon_0} \left(1 - \frac{x}{\sqrt{x^2 + R^2}}\right)$$where $\sigma$ is the surface charge density ($\sigma = \frac{Q}{\pi R^2}$), $Q$ is the total charge on the disk, $R$ is the radius of the disk, $x$ is the distance from the disk along its axis, and $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12} C^2/N \cdot m^2$).Given:- $Q = 3.00 \mu C = 3.00 \times 10^{-6} C$- $R = 30.0 cm = 0.30 m$- $x = 15.0 cm = 0.15 m$- $\epsilon_0 = 8.85 \times 10^{-12} C^2/N \cdot m^2$First, calculate the surface charge density $\sigma$:$\sigma = \frac{Q}{\pi R^2} = \frac{3.00 \times 10^{-6} C}{\pi (0.30 m)^2}$Then, substitute $\sigma$, $x$, $R$, and $\epsilon_0$ into the formula for $E$:$$E = \frac{\sigma}{2\epsilon_0} \left(1 - \frac{0.15 m}{\sqrt{(0.15 m)^2 + (0.30 m)^2}}\right)$$After performing the calculations, the result matches the value given in choice C, which is $3.31 \times 10^5 N/C$. This calculation involves integrating Coulomb's law over the disk's surface to account for the contributions of all the infinitesimal charge elements on the disk to the electric field at the point of interest.

Quiz 23: The Electric Field

A 3.0-μC positive point charge is located at the origin and a positive point charge is located at Find the coordinates of the point where the net electric field strength due to these charges is zero.

A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero?

Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-μC charge. Find the magnitude of the electric field at the center of the square. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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?

Two point charges, Q₁= -1.0 μC and Q₂= + 4.0 μC, are placed as shown in the figure. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The y component of the electric field, at the origin O, is closest to

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?

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?

Three equal negative point charges are placed at three of the corners of a square of side d. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

At a distance of 4.3 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A point charge Q = -500 nC and two unknown point charges, q₁ and q₂, are placed as shown in the figure. The electric field at the origin O, due to charges Q, q₁ and q₂, is equal to zero. The charge q₁ is closest to

A very long wire carries a uniform linear charge density of What is the electric field strength from the center of the wire at a point on the wire's perpendicular bisector? (ε₀ = 8.85 × 10^-12 C^2/N ∙ m²)

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?

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?

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the magnitude of electric field due to these charges at a point midway between them? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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?

Quiz 23: The Electric Field

A 3.0-μC positive point charge is located at the origin and a positive point charge is located at Find the coordinates of the point where the net electric field strength due to these charges is zero.

A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero?

Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-μC charge. Find the magnitude of the electric field at the center of the square. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

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?

Two point charges, Q1 = -1.0 μC and Q2 = + 4.0 μC, are placed as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) The y component of the electric field, at the origin O, is closest to

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?

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?

Three equal negative point charges are placed at three of the corners of a square of side d. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

At a distance of 4.3 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

A point charge Q = -500 nC and two unknown point charges, q1 and q2, are placed as shown in the figure. The electric field at the origin O, due to charges Q, q1 and q2, is equal to zero. The charge q1 is closest to

A very long wire carries a uniform linear charge density of What is the electric field strength from the center of the wire at a point on the wire's perpendicular bisector? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

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?

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?

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the magnitude of electric field due to these charges at a point midway between them? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

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 +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-μC charge. Find the magnitude of the electric field at the center of the square. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two point charges, Q₁= -1.0 μC and Q₂= + 4.0 μC, are placed as shown in the figure. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The y component of the electric field, at the origin O, is closest to

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?

Three equal negative point charges are placed at three of the corners of a square of side d. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

At a distance of 4.3 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A point charge Q = -500 nC and two unknown point charges, q₁ and q₂, are placed as shown in the figure. The electric field at the origin O, due to charges Q, q₁ and q₂, is equal to zero. The charge q₁ is closest to

A very long wire carries a uniform linear charge density of What is the electric field strength from the center of the wire at a point on the wire's perpendicular bisector? (ε₀ = 8.85 × 10^-12 C^2/N ∙ m²)

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the magnitude of electric field due to these charges at a point midway between them? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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?