Question 1

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 5.9 cm is approximately

Accepted Answer

Since the electric field inside a uniformly charged cylindrical shell is zero, the electric field at r = 5.9 cm, which is inside the cylinder, is also zero. Hence, the correct answer is option B) zero.

Question 2

The electric field for a spherical shell of charge is discontinuous by the amount _____ at a point where there is a surface charge density  $\sigma$.

Accepted Answer

The electric field for a spherical shell of charge is discontinuous by the amount F1F1F1S1F1F1F10₀/F1F1F1S1F1F1F10 at a point where there is a surface charge density F1F1F1S1F1F1F10. This is because the electric field is proportional to the charge density, and the charge density is discontinuous at the surface of the shell.

Question 3

For a uniformly charged spherical sphere of radius R carrying a total charge Q,calculate the electric field at a distance R/2 outside the sphere divided by the electric field at a distance R/2 inside the sphere.

Accepted Answer

For a uniformly charged spherical sphere, the electric field outside the sphere is given by:

E = kQ/r^2

where k is Coulomb's constant, Q is the total charge, and r is the distance from the center of the sphere.

At a distance R/2 outside the sphere:

E_outside = kQ/(R/2)^2 = 4kQ/R^2

Inside the sphere, the electric field is:

E_inside = kQr/R^3

where r is the distance from the center of the sphere. At a distance R/2 inside the sphere,

r = R/2

E_inside = kQ(R/2)/R^3 = kQ/2R^2

Now, we can calculate the ratio of the fields:

E_outside/E_inside = (4kQ/R^2)/(kQ/2R^2) = 8/1 = 8

Therefore, the answer is E) 8/9.

Question 4

Electrical conductors contain

Accepted Answer

Electrical conductors contain both free and bound electrons. Bound electrons are tightly held within the atoms and can't move around freely. Free electrons, on the other hand, are loosely bound to their atoms and are free to move throughout the material, making it a good electrical conductor.

Question 5

Use the figure for the next problem.  An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density 
-The electric at y = b where 0 < b < d is

Accepted Answer

The answer of Use the figure for the next problem....

Question 6

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 30 cm.

Accepted Answer

The answer of A non-conducting pipe has a uniform charge...

Question 7

A large,flat conducting plate has a surface charge density $\sigma$ = 8.0 $\times$ 10^-9 C/m² on one of its surfaces.What is the magnitude of the electric field 10 µm from this plate?

Accepted Answer

The electric field due to a large, flat conducting plate is given by:
E = σ/2ε₀
where σ is the surface charge density and ε₀ is the permittivity of free space.
Plugging in the given values, we get:
E = (8.0 × 10⁻⁹ C/m²) / (2 × 8.85 × 10⁻¹² C²/Nm²)
E = 0.90 × 10³ N/C = 0.90 kN/C
Thus, the correct answer is (C).

Question 8

A solid spherical conductor has a radius of 15 cm.The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C.What is the surface charge density  $\sigma$ on the sphere?

Accepted Answer

The answer of A solid spherical conductor has a radius...

Question 9

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 6.1 cm is approximately

Accepted Answer

The answer of An infinitely long cylindrical shell of radius...

Question 10

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 16 cm is approximately

Accepted Answer

The electric field due to a uniformly charged spherical shell at a point outside the shell can be found by using the expression:

E = k σ R / r^2

where k is the Coulomb constant, σ is the surface charge density, R is the radius of the spherical shell, and r is the distance from the center of the shell to the point where the electric field is being measured.

Substituting the given values, we get:

E = (9 × 10^9 Nm^2/C^2) × (9 × 10^(-9) C/m^2) × 0.09 m / (0.16 m)^2

E ≈ 0.53 kN/C

Therefore, the best choice is (E) with an explanation as shown above.

Question 11

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 9.1 cm is approximately

Accepted Answer

The electric field $E$ at a distance $r$ from the center of a uniformly charged spherical shell of radius $R$ and surface charge density $\sigma$ is given by $E = \frac{\sigma}{\varepsilon_0} $ for $r > R$, where $\varepsilon_0$ is the vacuum permittivity ($8.85 \times 10^{-12} \, C^2/N \cdot m^2$). Given $\sigma = 9.0 \, nC/m^2 = 9.0 \times 10^{-9} \, C/m^2$ and $r = 9.1 \, cm > R = 9.0 \, cm$, we calculate $E$ as follows:$$E = \frac{\sigma}{\varepsilon_0} = \frac{9.0 \times 10^{-9}}{8.85 \times 10^{-12}} \approx 1.0 \times 10^3 \, N/C$$Therefore, the electric field at $r = 9.1 \, cm$ is approximately $1.0 \, kN/C$.

Question 12

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 40 cm.

Accepted Answer

The answer of A non-conducting pipe has a uniform charge...

Question 13

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 8.9 cm is approximately

Accepted Answer

For a spherical shell with uniform surface charge density, the electric field inside the shell (r < radius of the shell) is zero due to the symmetry of the charge distribution. Since 8.9 cm is inside the shell of radius 9.0 cm, the electric field at that point is zero.

Question 14

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 10 cm is approximately

Accepted Answer

By Gauss's Law, the electric field at a distance r from an infinitely long cylindrical shell with uniform surface charge density σ is given by E = σ/(2ε0), where ε0 is the permittivity of free space. Plugging in the given values, we get E = (12 nC/m)/(2ε0 × 6 cm) = 1/10ε0 kN/C. At r = 10 cm, the electric field is approximately equal to E = 1/10ε0 kN/C × (6 cm/10 cm) = 0.81 kN/C. Therefore, the best choice is D.

Question 15

The electric field at the surface of a conductor

Accepted Answer

The electric field at the surface of a conductor is perpendicular to the surface and depends on the surface charge density, which is influenced by the total charge, the area, and the curvature of the conductor.

Question 16

Which diagram best represents the electric field along the y-axis?

Accepted Answer

The answer of Which diagram best represents the electric field...

Question 17

The electric field for an infinite plane of charge is discontinuous by the amount _____ at a point where there is a surface charge density  $\sigma$.

Accepted Answer

The electric field for an infinite plane of charge is given by E = σ/2ε0, where σ is the surface charge density and ε0 is the permittivity of free space. The electric field above the plane is E1 = σ/2ε0, while the electric field below the plane is E2 = -σ/2ε0. The discontinuity in the electric field is given by ΔE = E1 - E2 = σ/ε0. 
Therefore, the amount of discontinuity at a point where there is a surface charge density σ is σ/ε0. 
In the given options, only Option B has this expression (σ/ε0) for the amount of discontinuity.

Question 18

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 4.0 cm is approximately

Accepted Answer

For a spherical shell with uniform surface charge density, the electric field inside the shell (r < radius of the shell) is zero due to the symmetry of the problem and Gauss's law. Since 4.0 cm is inside the shell of radius 9.0 cm, the electric field at that point is zero.

Question 19

Use the figure for the next problem.  An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density 
-The electric at y = b where b > d is

Accepted Answer

The answer of Use the figure for the next problem....

Question 20

For a solid uniformly charged sphere of radius R,calculate the electric field at a distance R/2 outside the sphere,divided by the electric field at a distance R/2 inside the sphere.

Accepted Answer

Using Gauss's law, we can find that the electric field inside the sphere is given by:
E_inside = (1/3ε0) * (Q/R^3) * r^2, where Q is the total charge of the sphere and r is the distance from the center.

Similarly, the electric field outside the sphere is given by:
E_outside = (1/4πε0) * (Q/R^2) * (R^3/r^2), where Q is the total charge of the sphere, R is the radius of the sphere and r is the distance from the center.

Substituting r = R/2, we get:
E_inside = (2/27) * E_outside

Dividing the electric field outside the sphere by the electric field inside the sphere will give:
E_outside/E_inside = 27/2 = 8/9

Therefore, the best answer is E) 8/9.

Quiz 22: The Electric Field Ii: Continuous Charge Distributions

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 5.9 cm is approximately

The electric field for a spherical shell of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

For a uniformly charged spherical sphere of radius R carrying a total charge Q,calculate the electric field at a distance R/2 outside the sphere divided by the electric field at a distance R/2 inside the sphere.

Electrical conductors contain

Use the figure for the next problem. An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density -The electric at y = b where 0 < b < d is

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 30 cm.

A large,flat conducting plate has a surface charge density $\sigma$ = 8.0 $\times$ 10^-9 C/m² on one of its surfaces.What is the magnitude of the electric field 10 µm from this plate?

A solid spherical conductor has a radius of 15 cm.The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C.What is the surface charge density $\sigma$ on the sphere?

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 6.1 cm is approximately

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 16 cm is approximately

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 9.1 cm is approximately

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 40 cm.

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 8.9 cm is approximately

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 10 cm is approximately

The electric field at the surface of a conductor

Which diagram best represents the electric field along the y-axis?

The electric field for an infinite plane of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 4.0 cm is approximately

Use the figure for the next problem. An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density -The electric at y = b where b > d is

For a solid uniformly charged sphere of radius R,calculate the electric field at a distance R/2 outside the sphere,divided by the electric field at a distance R/2 inside the sphere.

Quiz 22: The Electric Field Ii: Continuous Charge Distributions

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density σ\sigmaσ = 12 nC/m2.The electric field at r = 5.9 cm is approximately

The electric field for a spherical shell of charge is discontinuous by the amount _____ at a point where there is a surface charge density σ\sigmaσ .

For a uniformly charged spherical sphere of radius R carrying a total charge Q,calculate the electric field at a distance R/2 outside the sphere divided by the electric field at a distance R/2 inside the sphere.

Electrical conductors contain

Use the figure for the next problem. An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density -The electric at y = b where 0 < b < d is

A non-conducting pipe has a uniform charge density of 50 C/m3.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 30 cm.

A large,flat conducting plate has a surface charge density σ\sigmaσ = 8.0 ×\times× 10-9 C/m2 on one of its surfaces.What is the magnitude of the electric field 10 µm from this plate?

A solid spherical conductor has a radius of 15 cm.The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C.What is the surface charge density σ\sigmaσ on the sphere?

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density σ\sigmaσ = 12 nC/m2.The electric field at r = 6.1 cm is approximately

A spherical shell of radius 9.0 cm carries a uniform surface charge density σ\sigmaσ = 9.0 nC/m2.The electric field at r = 16 cm is approximately

A spherical shell of radius 9.0 cm carries a uniform surface charge density σ\sigmaσ = 9.0 nC/m2.The electric field at r = 9.1 cm is approximately

A non-conducting pipe has a uniform charge density of 50 C/m3.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 40 cm.

A spherical shell of radius 9.0 cm carries a uniform surface charge density σ\sigmaσ = 9.0 nC/m2.The electric field at r = 8.9 cm is approximately

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density σ\sigmaσ = 12 nC/m2.The electric field at r = 10 cm is approximately

The electric field at the surface of a conductor

Which diagram best represents the electric field along the y-axis?

The electric field for an infinite plane of charge is discontinuous by the amount _____ at a point where there is a surface charge density σ\sigmaσ .

A spherical shell of radius 9.0 cm carries a uniform surface charge density σ\sigmaσ = 9.0 nC/m2.The electric field at r = 4.0 cm is approximately

Use the figure for the next problem. An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density -The electric at y = b where b > d is

For a solid uniformly charged sphere of radius R,calculate the electric field at a distance R/2 outside the sphere,divided by the electric field at a distance R/2 inside the sphere.

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 5.9 cm is approximately

The electric field for a spherical shell of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 30 cm.

A large,flat conducting plate has a surface charge density $\sigma$ = 8.0 $\times$ 10^-9 C/m² on one of its surfaces.What is the magnitude of the electric field 10 µm from this plate?

A solid spherical conductor has a radius of 15 cm.The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C.What is the surface charge density $\sigma$ on the sphere?

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 6.1 cm is approximately

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 16 cm is approximately

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 9.1 cm is approximately

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 40 cm.

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 8.9 cm is approximately

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 10 cm is approximately

The electric field for an infinite plane of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 4.0 cm is approximately