Question 1

A cube of side 3.56 cm has a charge of 9.11 μC placed at its center. Calculate the electric flux through one side of the cube.

Accepted Answer

We can use Gauss' law to find the electric flux through one side of the cube. Gauss' law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface.

Since the cube has symmetry, we can use a cube with one face as our closed surface. The charge enclosed by this cube is simply the charge at the center, which is 9.11 μC.

The area of one face of the cube is (3.56 cm)^2 = 12.6736 cm^2 = 0.00126736 m^2.

Thus, the electric flux through one side of the cube is:

Φ = E x A = Q/ε0 x A

where ε0 is the permittivity of free space.

Φ = (9.11 × 10^-6 C) / (8.85 × 10^-12 N^-1 m^-2 C^2) x 0.00126736 m^2
Φ = 1.72 × 10^15 N m^2/C

Therefore, the answer is D.

Question 2

Consider a uniform electric field E= 5.0 kN/C) parallel to the +x axis. What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x-axis?

Accepted Answer

The answer of Consider a uniform electric field E= 5.0...

Question 3

A rod of infinite length has a charge per unit length of λ = q/l). Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = 4π₀)^-¹,

Accepted Answer

The answer of  A rod of infinite length has...

Question 4

An electric field is E = 400 N/C) for x > 0 and E = -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the net charge inside the cylinder?

Accepted Answer

The answer of An electric field is E = 400...

Question 5

Which of the following circumstances about Gauss's law is true?

Accepted Answer

Gauss's law is universally applicable to any closed surface, regardless of symmetry or shape, and can be used for point charges, multiple charges, and symmetric charge distributions.

Question 6

An electric field is E= 400 N/C) for x > 0 and E= -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the flux through each end of the cylinder?

Accepted Answer

The answer of An electric field is E= 400 N/C)...

Question 7

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀)^-¹?

Accepted Answer

By Gauss's law, since the electric field is a conservative field, it is determined uniquely by the total charge enclosed within the Gaussian surface. For any radius r < a, the Gaussian surface completely encloses the solid sphere, which has a charge of +Q. Since the hollow sphere is concentric with the solid sphere, it does not contribute to the electric field at this radius. Therefore, the total charge enclosed is +Q, and Gauss's law gives us:

∫E·dA = Q/ε0

E·4πr^2 = Q/ε0

E = Q/(4πε0r^2)

which shows that the electric field at radius r is inversely proportional to r^2, and thus it approaches infinity as r approaches zero. However, this calculation does not depend on the charge on the hollow sphere, which is irrelevant for calculating the electric field at this radius. Therefore, the electric field at radius r is independent of the charge on the hollow sphere, and is given by choice E, which is zero.

Question 8

A horizontal surface of area 0.321 m² has an electric flux of 123 N.m²/C passing through it at an angle of 25° to the horizontal. If the flux is due to a uniform electric field, calculate the magnitude of the latter.

Accepted Answer

The electric flux through a surface is given by the product of the electric field strength and the area of the surface perpendicular to the field. In this case, the area perpendicular to the field is the area of the surface multiplied by the cosine of the angle between the field and the normal to the surface. Therefore, the electric field strength is given by:E = Φ/Acosθ = 123 N.m2/C / (0.321 m2cos25°) = 907 N m2/CTherefore, the correct answer is A.

Question 9

A hollow spherical shell of radius 5.36 cm has a charge of 1.91 μC placed at its center. Calculate the electric flux through an area of 1.20 × 10^-² m² on the shell.

Accepted Answer

The answer of A hollow spherical shell of radius 5.36...

Question 10

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀)^-¹?

Accepted Answer

The answer of  A solid sphere of radius a...

Question 11

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where a < r < b, is which of the following, in terms of k = 4π₀)^-¹?

Accepted Answer

The answer of  A solid sphere of radius a...

Question 12

The figure shows a surface enclosing the charges 2q and -q. The net flux through the surface surrounding the two charges is

Accepted Answer

The answer of  The figure shows a surface enclosing...

Question 13

The figure shows a surface enclosing the charges q and -q. The net flux through the surface surrounding the two charges is

Accepted Answer

The net charge enclosed by the surface is zero (q + (-q) = 0). Therefore, by Gauss's law, the net flux through the surface is also zero.

Question 14

A sphere of radius 8.0 cm carries a uniform volume charge density ρ= 500 nC/m³. What is the electric field at r = 7.9 cm?

Accepted Answer

The answer of A sphere of radius 8.0 cm carries...

Question 15

A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nC/m³. What is the electric field at r = 3.0 cm?

Accepted Answer

First, we need to find the charge enclosed within the sphere of radius 3.0 cm. Since the charge density is uniform, we can use
ρ = Q/V ,
where V is the volume of the sphere. Thus,
Q = ρV = (500 nC/m3) (4/3π(0.03 m)3) = 0.566 nC.
Now, we can use Gauss's Law to find the electric field at r = 3.0 cm. Since the sphere has spherical symmetry, we choose a spherical Gaussian surface with radius 3.0 cm. The electric field is then given by
E = Qenc/ε0A,
where Qenc is the charge enclosed by the Gaussian surface, ε0 is the permittivity of free space, and A is the area of the Gaussian surface. Since the electric field is radial, the area of the Gaussian surface is simply 4πr2. Thus,
E = (0.566 nC)/(8.85×10-12 N-1C2)(4π(0.03 m)2) = 564.7 N/C ≈ 565 N/C.

Question 16

The figure shows a surface, S, with two charges q and -2q. The net flux through the surface is

Accepted Answer

The net flux through the surface is given by the electric flux through the surface due to the positive charge plus the electric flux through the surface due to the negative charge. Since the surface is closed, the total electric flux through the surface is zero according to Gauss's law, which states that the total electric flux through a closed surface is proportional to the net charge enclosed by the surface. Thus, the answer is zero.

Question 17

Consider a uniform electric field E = 5.0 kN/C) parallel to the +x-axis. What is the flux of this field through a square of side 20 cm in a plane parallel to the yz plane?

Accepted Answer

The electric flux through a surface is given by the formula Φ = E · A · cos(θ), where E is the electric field strength, A is the area of the surface, and θ is the angle between the field and the normal to the surface. Here, E = 5.0 kN/C, the side of the square is 0.20 m, so A = 0.20 m * 0.20 m = 0.04 m². Since the field is parallel to the +x-axis and the square is parallel to the yz plane, θ = 0°, and cos(0°) = 1. Thus, Φ = 5.0 kN/C * 0.04 m² * 1 = 0.20 kN·m²/C.

Question 18

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r > b, is which of the following, in terms of k = 4π₀)^-¹?

Accepted Answer

Since the point of interest is outside the larger, negatively charged sphere, there is no net charge contained within the sphere surrounding that point. Therefore, by Gauss's Law, the electric field at this point is zero.

Question 19

An electric field is E = 400 N/C) for x > 0 and E = -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the net outward flux through the entire cylindrical surface?

Accepted Answer

The answer of An electric field is E = 400...

Question 20

A hollow metal sphere has a total charge of 100 µC. If the radius of the sphere is 50 cm, the electric field intensity at a distance of 3.0 m from the surface of the sphere is approximately

Accepted Answer

The answer of A hollow metal sphere has a total...

Quiz 16: Electrostatics I: Electric Charge, Forces, and Fields

A cube of side 3.56 cm has a charge of 9.11 μC placed at its center. Calculate the electric flux through one side of the cube.

Consider a uniform electric field E= 5.0 kN/C) parallel to the +x axis. What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x-axis?

A rod of infinite length has a charge per unit length of λ = q/l) . Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = 4π₀) ^-¹,

An electric field is E = 400 N/C) for x > 0 and E = -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the net charge inside the cylinder?

Which of the following circumstances about Gauss's law is true?

An electric field is E= 400 N/C) for x > 0 and E= -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the flux through each end of the cylinder?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀) ^-¹?

A horizontal surface of area 0.321 m² has an electric flux of 123 N.m²/C passing through it at an angle of 25° to the horizontal. If the flux is due to a uniform electric field, calculate the magnitude of the latter.

A hollow spherical shell of radius 5.36 cm has a charge of 1.91 μC placed at its center. Calculate the electric flux through an area of 1.20 × 10^-² m² on the shell.

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀) ^-¹?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where a < r < b, is which of the following, in terms of k = 4π₀) ^-¹?

The figure shows a surface enclosing the charges 2q and -q. The net flux through the surface surrounding the two charges is

The figure shows a surface enclosing the charges q and -q. The net flux through the surface surrounding the two charges is

A sphere of radius 8.0 cm carries a uniform volume charge density ρ= 500 nC/m³. What is the electric field at r = 7.9 cm?

A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nC/m³. What is the electric field at r = 3.0 cm?

The figure shows a surface, S, with two charges q and -2q. The net flux through the surface is

Consider a uniform electric field E = 5.0 kN/C) parallel to the +x-axis. What is the flux of this field through a square of side 20 cm in a plane parallel to the yz plane?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r > b, is which of the following, in terms of k = 4π₀) ^-¹?

A hollow metal sphere has a total charge of 100 µC. If the radius of the sphere is 50 cm, the electric field intensity at a distance of 3.0 m from the surface of the sphere is approximately

Quiz 16: Electrostatics I: Electric Charge, Forces, and Fields

A cube of side 3.56 cm has a charge of 9.11 μC placed at its center. Calculate the electric flux through one side of the cube.

Consider a uniform electric field E= 5.0 kN/C) parallel to the +x axis. What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x-axis?

A rod of infinite length has a charge per unit length of λ = q/l) . Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = 4π0) -1,

An electric field is E = 400 N/C) for x > 0 and E = -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the net charge inside the cylinder?

Which of the following circumstances about Gauss's law is true?

An electric field is E= 400 N/C) for x > 0 and E= -400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x-axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the flux through each end of the cylinder?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π0) -1?

A horizontal surface of area 0.321 m2 has an electric flux of 123 N.m2/C passing through it at an angle of 25° to the horizontal. If the flux is due to a uniform electric field, calculate the magnitude of the latter.

A hollow spherical shell of radius 5.36 cm has a charge of 1.91 μC placed at its center. Calculate the electric flux through an area of 1.20 × 10-2 m2 on the shell.

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π0) -1?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where a < r < b, is which of the following, in terms of k = 4π0) -1?

The figure shows a surface enclosing the charges 2q and -q. The net flux through the surface surrounding the two charges is

The figure shows a surface enclosing the charges q and -q. The net flux through the surface surrounding the two charges is

A sphere of radius 8.0 cm carries a uniform volume charge density ρ= 500 nC/m3. What is the electric field at r = 7.9 cm?

A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nC/m3. What is the electric field at r = 3.0 cm?

The figure shows a surface, S, with two charges q and -2q. The net flux through the surface is

Consider a uniform electric field E = 5.0 kN/C) parallel to the +x-axis. What is the flux of this field through a square of side 20 cm in a plane parallel to the yz plane?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r > b, is which of the following, in terms of k = 4π0) -1?

A hollow metal sphere has a total charge of 100 µC. If the radius of the sphere is 50 cm, the electric field intensity at a distance of 3.0 m from the surface of the sphere is approximately

A rod of infinite length has a charge per unit length of λ = q/l) . Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = 4π₀) ^-¹,

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀) ^-¹?

A horizontal surface of area 0.321 m² has an electric flux of 123 N.m²/C passing through it at an angle of 25° to the horizontal. If the flux is due to a uniform electric field, calculate the magnitude of the latter.

A hollow spherical shell of radius 5.36 cm has a charge of 1.91 μC placed at its center. Calculate the electric flux through an area of 1.20 × 10^-² m² on the shell.

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = 4π₀) ^-¹?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where a < r < b, is which of the following, in terms of k = 4π₀) ^-¹?

A sphere of radius 8.0 cm carries a uniform volume charge density ρ= 500 nC/m³. What is the electric field at r = 7.9 cm?

A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nC/m³. What is the electric field at r = 3.0 cm?

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a charge +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r > b, is which of the following, in terms of k = 4π₀) ^-¹?