Question 1

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

D

Question 2

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 electric field due to a point charge is given by:$$E = k\frac{q}{r^2}$$where:* k is Coulomb's constant (8.99 × 10^9 N ∙ m^2/C^2)* q is the charge (in Coulombs)* r is the distance from the charge (in meters)In this problem, we have two point charges:* q1 = +20.0 μC = +20.0 × 10^-6 C* q2 = -8.00 μC = -8.00 × 10^-6 CThe distance between the charges is:* r = 20.0 cm = 0.200 mThe point at which we want to find the electric field is midway between the charges, so the distance from each charge to the point is:* r1 = r2 = 0.100 mThe electric field due to q1 at the point is:$$E1 = k\frac{q1}{r1^2} = (8.99 × 10^9 N ∙ m^2/C^2)\frac{20.0 × 10^-6 C}{(0.100 m)^2} = 17.98 × 10^6 N/C$$The electric field due to q2 at the point is:$$E2 = k\frac{q2}{r2^2} = (8.99 × 10^9 N ∙ m^2/C^2)\frac{-8.00 × 10^-6 C}{(0.100 m)^2} = -7.19 × 10^6 N/C$$The net electric field at the point is the vector sum of E1 and E2:$$E = E1 + E2 = 17.98 × 10^6 N/C - 7.19 × 10^6 N/C = 25.2 × 10^6 N/C$$The electric field is directed toward the negative charge, so the correct answer is A.

Question 3

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

A

Question 4

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 have field lines extending outwards from them, indicating that they are positive charges. On the other hand, the charge Q₂ has field lines terminating on it, indicating that it is a negative charge. Therefore, the signs of the three charges are: Q₁ is positive, Q₂ is negative, and Q₃ is positive. The correct answer is (A).

Question 5

A very long wire carries a uniform linear charge density of 7.0 nC/m. What is the electric field strength 16.0 m 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 electric field due to an infinite line of charge is given by E = (λ / (2πε₀r)), where λ is the linear charge density, ε₀ is the permittivity of free space, and r is the distance from the wire. Substituting the given values, E = (7.0 × 10⁻⁹ C/m) / (2π × 8.85 × 10⁻¹² C²/N·m² × 16.0 m) ≈ 7.9 N/C.

Question 6

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 7

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

Since all three charges are negative and symmetrical, the electric fields due to the two charges that are diagonal to the center of the square cancel out, leaving only the electric field due to the charge directly opposite to the center. This electric field points towards the center of the square, as shown in option C. Therefore, the net electric field at the center of the square points towards the center of the square, which is represented by option C.

Question 8

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

The answer of A long, thin rod parallel to the...

Question 9

A 3.0-μC positive point charge is located at the origin and a 2.0 μC positive point charge is located at x = 0.00 m, y = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is zero.

Accepted Answer

The answer of A 3.0-μC positive point charge is located...

Question 10

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 11

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 12

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

The answer of Two thin 80.0-cm rods are oriented at...

Question 13

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 14

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 15

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 16

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 17

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.

Question 18

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 19

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 20

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,...

Quiz 26: The Electric Field

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= -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?

A very long wire carries a uniform linear charge density of 7.0 nC/m. What is the electric field strength 16.0 m from the center of the wire at a point on the wire's perpendicular bisector? (ε₀ = 8.85 × 10^-12 C^2/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

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?

A 3.0-μC positive point charge is located at the origin and a 2.0 μC positive point charge is located at x = 0.00 m, y = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is zero.

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)

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

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?

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?

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. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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)

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?

Quiz 26: The Electric Field

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 = -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?

A very long wire carries a uniform linear charge density of 7.0 nC/m. What is the electric field strength 16.0 m from the center of the wire at a point on the wire's perpendicular bisector? (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

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?

A 3.0-μC positive point charge is located at the origin and a 2.0 μC positive point charge is located at x = 0.00 m, y = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is zero.

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)

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

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?

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?

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. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

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)

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?

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= -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?

A very long wire carries a uniform linear charge density of 7.0 nC/m. What is the electric field strength 16.0 m from the center of the wire at a point on the wire's perpendicular bisector? (ε₀ = 8.85 × 10^-12 C^2/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

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)

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. What is the magnitude of the net electric field at the center of the square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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)