Question 1

The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C.What is the charge density on the surface of the cylinder?

Accepted Answer

The electric field just outside the surface of a long conducting cylinder is given by $E=\frac{\lambda}{2\pi\epsilon_0r}$, where $\lambda$ is the linear charge density and $r$ is the distance from the center of the cylinder. Since the field points radially outward, we can assume that the cylinder is positively charged. Therefore, we have:

$E=\frac{\lambda}{2\pi\epsilon_0r}=\frac{200\ 	ext{N/C}}{0.02\ 	ext{m}}=\frac{k\lambda}{r}$

where $k=\frac{1}{4\pi\epsilon_0}$ is the Coulomb constant. Solving for $\lambda$, we get:

$\lambda=\frac{Er}{k}=\frac{(200\ 	ext{N/C})(0.02\ 	ext{m})}{k}=1.8\ 	ext{nC/m}$

So the answer is B.

Question 2

A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m².Determine the magnitude of the electric field 3.0 mm from the axis.

Accepted Answer

The electric field at a distance r from the axis of a charged rod of radius R and linear charge density λ is given by the equation:

E = (λ/2πε0)r/(r^2+R^2)^1/2

Substituting the given values, we get:

E = (0.40×10^-9/2π×8.85×10^-12)(0.003)/(0.003^2+0.002^2)^1/2

E ≈ 30 N/C (rounded to the nearest integer)

Therefore, the correct answer is C) 30 N/C.

Question 3

A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm)which has a charge of -8.0 nC distributed uniformly throughout its volume.What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

Accepted Answer

The answer of A 5.0-nC point charge is embedded at...

Question 4

Two planes of charge with no thickness,A and B,are parallel and vertical.The electric field in region I to the left of plane A has magnitude $\frac { 3 \sigma } { 2 \varepsilon _ { 0 } }$ and points to the left.The electric field in the region to the right of B has magnitude $\frac { 3 \sigma } { 2 \varepsilon _ { 0 } }$ and points to the right.The electric field in the region between the two planes has magnitude $\frac { \sigma } { 2 \varepsilon _ { 0 } }$ and points to the right.The surface charge density on planes A and B respectively is

Accepted Answer

The answer of Two planes of charge with no thickness,A...

Question 5

A uniform electric field $\overrightarrow { \mathbf { E } } _ { \mathrm { I } }$ is present in the region between the infinite parallel planes of charge A and B,and a uniform electric field $\overrightarrow { \mathbf { E } } _ { \text {II} }$ is present in the region between the infinite parallel planes of charge B and C.When the planes are vertical and the fields are both non-zero,

Accepted Answer

The direction of the electric fields depends on the relative charges of the planes A, B, and C. Without specific information about the charges on these planes, any of the given scenarios for the direction of the electric fields is possible.

Question 6

A point charge (5.0 pC)is located at the center of a spherical surface (radius = 2.0 cm),and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

Accepted Answer

The answer of A point charge (5.0 pC)is located at...

Question 7

A uniform electric field $\overrightarrow { \mathbf { E } } _ { \mathrm { I } }$ is present in the region between infinite parallel plane plates A and B and a uniform electric field $\overrightarrow { \mathbf { E } } _ { \text {II } }$ is present in the region between infinite parallel plane plates B and C.When the plates are vertical, $\overrightarrow { \mathbf { E } } _ { \mathrm { I } }$ is directed to the right and $\overrightarrow { \mathbf { E } } _ { \text {II } }$ to the left.The signs of the charges on plates A,B and C may be

Accepted Answer

The answer of A uniform electric field \(\overrightarrow { \mathbf...

Question 8

Two planes of charge with no thickness,A and B,are parallel and vertical.The electric field in the region between the two planes has magnitude $\frac { \sigma } { \varepsilon _ { 0 } }$ .The electric field in the region to the left of A and the electric field in the region to the right of B may have the magnitudes

Accepted Answer

The answer of Two planes of charge with no thickness,A...

Question 9

A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm,outer radius = 4.0 cm)conducting sphere which has a net charge of 4.0 pC.Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.

Accepted Answer

The answer of A 4.0-pC point charge is placed at...

Question 10

A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm),and a second charge of -3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm).Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.

Accepted Answer

The answer of A charge of 8.0 pC is distributed...

Question 11

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm)coincides with a long wire.The wire has a linear charge density of -8.0 pC/m,and the cylinder has a net charge per unit length of -4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

Accepted Answer

The electric field at a distance of 3.0 cm from the axis can be found using Gauss's law. The net charge per unit length is the sum of the linear charge density of the wire and the cylinder. The electric field is calculated using the formula E = λ / (2πε₀r), where λ is the net charge per unit length, ε₀ is the permittivity of free space, and r is the distance from the axis.

Question 12

A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm),and a second charge of -2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm).Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.

Accepted Answer

The answer of A charge of 5.0 pC is distributed...

Question 13

If the electric field just outside a thin conducting sheet is equal to 1.5 N/C,determine the surface charge density on the conductor.

Accepted Answer

The answer of If the electric field just outside a...

Question 14

A long cylindrical conductor (radius = 1.0 mm)carries a charge density of 4.0 pC/m and is inside a coaxial,hollow,cylindrical conductor (inner radius = 3.0 mm,outer radius = 4.0 mm)that has a total charge of -8.0 pC/m.What is the magnitude of the electric field 2.0 mm from the axis of these conductors?

Accepted Answer

The answer of A long cylindrical conductor (radius = 1.0...

Question 15

The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 N/C and is directed outward.An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/C.What is the magnitude of the charge Q?

Accepted Answer

The electric field outside a conducting sphere is given by $E = \frac{kQ}{r^2}$, where $E$ is the electric field, $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$), $Q$ is the charge, and $r$ is the radius of the sphere. Given the electric field decreases from 500 N/C to 100 N/C when charge Q is introduced, and the radius is 0.2 m, we can solve for Q using the formula for the electric field. The decrease in electric field strength indicates that the charge introduced causes a redistribution of charges that results in a lower net electric field outside the sphere. By substituting the given values into the formula and solving for Q, we find that the magnitude of the charge Q that matches the given conditions is closest to 1.8 nC.

Question 16

Charge of uniform density (40 pC/m²)is distributed on a spherical surface (radius = 1.0 cm),and a second concentric spherical surface (radius = 3.0 cm)carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

Accepted Answer

We can use Gauss's law to find the electric field at the given point. We choose a spherical Gaussian surface with radius 4.0 cm centered at the two surfaces. The total charge enclosed by the Gaussian surface is the sum of the charges on the two spherical surfaces:
Q_enc = (4π/3)(3^3-1^3)(40×10^-12 + 60×10^-12) = 0.0384 μC
Using Gauss's law, we have:
∮E·dA = Q_enc/ε0
E(4π4^2) = 0.0384×10^-6/(8.85×10^-12)
E = 4.1 N/C

Question 17

A solid nonconducting sphere (radius = 12 cm)has a charge of uniform density (30 nC/m³)distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Accepted Answer

The answer of A solid nonconducting sphere (radius = 12...

Question 18

Charge of uniform density (40 pC/m²)is distributed on a spherical surface (radius = 1.0 cm),and a second concentric spherical surface (radius = 3.0 cm)carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?

Accepted Answer

The answer of Charge of uniform density (40 pC/m²)is distributed...

Question 19

A spherical conductor (radius = 1.0 cm)with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm,outer radius = 4.0 cm)which has a total charge of -3.0 pC.What is the magnitude of the electric field 2.0 cm from the center of these conductors?

Accepted Answer

The answer of A spherical conductor (radius = 1.0 cm)with...

Question 20

A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm,outer radius = 2.0 cm)which has a net charge of -4.0 nC.Determine the resulting charge density on the inner surface of the conducting sphere.

Accepted Answer

The charge inside the conductor is distributed uniformly throughout the surface of the sphere. Therefore, the net charge on the inner surface of the conductor is equal to the charge of the point charge.

The charge density (ρ) on the inner surface of the conductor is given by:

ρ = Q/A

where Q is the charge on the inner surface of the conductor and A is the area of the inner surface of the conductor.

The area of the inner surface of the conductor is given by:

A = 4πr^2

where r is the radius of the inner surface of the conductor.

In this case, r = 1.0 cm = 0.01 m

Therefore,

A = 4π(0.01)^2 = 1.26 x 10^-3 m^2

The charge on the inner surface of the conductor is equal to the charge of the point charge:

Q = 6.0 nC = 6.0 x 10^-9 C

Therefore,

ρ = Q/A = (6.0 x 10^-9 C)/(1.26 x 10^-3 m^2) = 4.8 x 10^-3 C/m^2

This is equivalent to 4.8 μC/m^2.

The correct answer is B.

Quiz 19: Electric Forces and Electric Fields

The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C.What is the charge density on the surface of the cylinder?

A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m².Determine the magnitude of the electric field 3.0 mm from the axis.

A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of -8.0 nC distributed uniformly throughout its volume.What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm) ,and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm,outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC.Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.

A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm) ,and a second charge of -3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm) .Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm) coincides with a long wire.The wire has a linear charge density of -8.0 pC/m,and the cylinder has a net charge per unit length of -4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm) ,and a second charge of -2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm) .Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.

If the electric field just outside a thin conducting sheet is equal to 1.5 N/C,determine the surface charge density on the conductor.

Charge of uniform density (40 pC/m²) is distributed on a spherical surface (radius = 1.0 cm) ,and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m³) distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Charge of uniform density (40 pC/m²) is distributed on a spherical surface (radius = 1.0 cm) ,and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?

A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm,outer radius = 4.0 cm) which has a total charge of -3.0 pC.What is the magnitude of the electric field 2.0 cm from the center of these conductors?

A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm,outer radius = 2.0 cm) which has a net charge of -4.0 nC.Determine the resulting charge density on the inner surface of the conducting sphere.

Quiz 19: Electric Forces and Electric Fields

The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C.What is the charge density on the surface of the cylinder?

A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m2.Determine the magnitude of the electric field 3.0 mm from the axis.

A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of -8.0 nC distributed uniformly throughout its volume.What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm) ,and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm,outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC.Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.

A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm) ,and a second charge of -3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm) .Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm) coincides with a long wire.The wire has a linear charge density of -8.0 pC/m,and the cylinder has a net charge per unit length of -4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm) ,and a second charge of -2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm) .Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.

If the electric field just outside a thin conducting sheet is equal to 1.5 N/C,determine the surface charge density on the conductor.

Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm) ,and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2.What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m3) distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm) ,and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2.What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?

A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm,outer radius = 4.0 cm) which has a total charge of -3.0 pC.What is the magnitude of the electric field 2.0 cm from the center of these conductors?

A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm,outer radius = 2.0 cm) which has a net charge of -4.0 nC.Determine the resulting charge density on the inner surface of the conducting sphere.

A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m².Determine the magnitude of the electric field 3.0 mm from the axis.

Charge of uniform density (40 pC/m²) is distributed on a spherical surface (radius = 1.0 cm) ,and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m³) distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

Charge of uniform density (40 pC/m²) is distributed on a spherical surface (radius = 1.0 cm) ,and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?