Question 1

Which one of the following cannot be a statement of Gauss's Law for some physical situation?

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Question 2

A constant electric field Is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm.The electric flux through the plane's surface,in N ⋅ m²/C,is

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The answer of A constant electric field 
Is present throughout...

Question 3

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

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Question 4

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

Since the system is symmetric around the axis, we can use Gauss's Law to find the electric field.

Consider a cylindrical Gaussian surface of radius 2.0 mm and height L (which we will take to infinity). By symmetry, the electric field is perpendicular to the surface at every point on it, and has the same magnitude at every point on a given circle.

The electric field magnitude at a point distance r from the axis is given by:

E = (1/2ε₀)(q_enclosed / πr²),

where ε₀ is the permittivity of free space, and q_enclosed is the charge enclosed inside the Gaussian surface.

The charge enclosed by the Gaussian surface includes the charge inside the smaller cylinder and also the charge on the inner surface of the larger cylinder. The charge on the outer surface of the larger cylinder does not contribute since it is outside the Gaussian surface.

The total charge q_enclosed is:

q_enclosed = q_small + q_inner,

where

q_small = λ_small x L = λ_small x π(0.001 m)²,

q_inner = λ_inner x L = λ_inner x π[(0.004 m)² - (0.003 m)²].

Substituting in the values, we get:

q_small = (4 pC/m)(π(0.001 m)²) = 1.2566 x 10^-8 C

q_inner = (-8 pC/m)(π[(0.004 m)² - (0.003 m)²]) = -2.5132 x 10^-8 C

q_enclosed = -1.2566 x 10^-8 C

Therefore,

E = (1/2ε₀)(q_enclosed / πr²) = (1/2ε₀)(-1.2566 x 10^-8 C / π(0.002 m)²)

= 35.98 N/C ≈ 36 N/C

So the answer is D.

Question 5

When a cube is inscribed in a sphere of radius r,the length L of a side of the cube is )If a positive point charge Q is placed at the center of the spherical surface,the ratio of the electric flux Φ_sphere at the spherical surface to the flux Φ_cube at the surface of the cube is

Accepted Answer

Since the charge is at the center, the electric field lines will be radially outward and perpendicular to the surface of the sphere and the cube. Therefore, the electric flux through both surfaces will be proportional to the areas of the surfaces. 
Since the cube is inscribed in the sphere, the diameter of the sphere is equal to the diagonal of the cube, which is L√3. Thus, the radius of the sphere is r = (L/2)√3. The surface area of the sphere is 4πr^2 and the surface area of the cube is 6L^2. 
Thus, the ratio of the flux at the surface of the sphere to the flux at the surface of the cube is

Φ_sphere / Φ_cube = (4πr^2) / (6L^2) = (4π/3) (L/2)^2 / (L^2) = (2/3) π

This ratio is independent of the radius of the sphere and the length of the side of the cube, and depends only on the geometry of the problem. Therefore, the correct answer is (C) 1.

Question 6

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 induces an equal but opposite charge on the inner surface to maintain electrostatic equilibrium. Thus, the inner surface will have a charge of -6.0 nC to neutralize the effect of the +6.0 nC point charge. The choice of units in the options seems to be a mistake (μC/m²), but the correct concept is that the inner surface charge density is equal in magnitude but opposite in sign to the point charge placed at the center.

Question 7

Three originally uncharged infinite parallel planes are arranged as shown.Then the upper plate has surface charge density σ placed on it while the lower plate receives surface charge density −σ.The net charge induced on the center plate is

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Question 8

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.Then charge +3q is placed on the outside of the shell.When static equilibrium is reached,the charges on the inner and outer surfaces of the shell are respectively

Accepted Answer

When a charge is placed inside a conducting shell, the inner surface of the shell acquires a charge equal in magnitude but opposite in sign to the enclosed charge to ensure the electric field inside the conductor is zero. Thus, the inner surface gets a charge of +q to neutralize the effect of the −q charge inside. When +3q is placed on the outside, the total charge on the shell must equal +3q. Since the inner surface already has +q, the outer surface must have +2q to make the total charge on the shell +3q.

Question 9

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 cylinder is given by:

E = (λ/2πεr)

where λ is the charge density on the surface of the cylinder, ε is the permittivity of free space, and r is the distance from the axis of the cylinder to the point where the electric field is being measured.

In this case, r = 2.0 cm = 0.02 m and E = 200 N/C. Substituting these values into the equation above, we get:

200 N/C = (λ/2πε)(1/0.02 m)

Solving for λ, we get:

λ = (200 N/C)(0.02 m)(2πε) = 1.8 nC/m

Therefore, the answer is B, 1.8 nC/m.

Question 10

An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station.Which statement is correct?

Accepted Answer

The astronaut does not need to worry because, according to the principle of electrostatic shielding, in a charged conductor, the excess charge resides on the outer surface, leaving the electric field inside the conductor (and thus inside the chamber) zero. This means the astronaut inside the all-metal chamber is unaffected by the external charge.

Question 11

An uncharged metal sphere is placed on an insulating puck on a frictionless table.While being held parallel to the table,a rod with a charge q is brought close to the sphere,but does not touch it.As the rod is brought in,the sphere

Accepted Answer

When the charged rod is brought near the uncharged metal sphere, the electrons within the sphere will be repelled by the like charge on the rod, causing them to move away from the rod and toward the opposite side of the sphere. This creates an induced charge separation in the sphere, leaving the side closest to the rod with a net positive charge and the opposite side with a net negative charge. This results in an attractive force between the rod and the sphere, causing the sphere to move toward the rod.

Question 12

A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread.The sphere is given a negative charge before the cover is placed on the bucket.The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket.Which statement is correct?

Accepted Answer

When a charged object comes into contact with a conductor, the charge redistributes over the surface of the conductor. In this case, since the bucket and cover are conductive, the negative charge on the sphere will spread over the outer surfaces of the bucket and cover, not remaining localized on the sphere or spreading equally over the inside surfaces or the sphere itself.

Question 13

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?

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Question 14

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

First, we can use Gauss's law to find the charge on the sphere without the introduction of Q. Since the electric field is uniform just outside the surface of the sphere, we know that the electric flux through any closed surface just outside the sphere is:

Φ = E*A = (500 N/C)*(4π*(0.2 m)^2) = 100π N m^2/C

(Since the electric field is perpendicular to the surface, the cosine of the angle between E and A is 1 and is unnecessary to include in the calculation).

Gauss's law tells us that this flux is also equal to the total charge enclosed by the surface divided by ε0, the permittivity of free space:

Φ = Qenc/ε0

For a conducting sphere, all the charge resides on the surface, so Qenc is just the charge on the sphere:

Qenc = Qsphere

Combining these two equations:

Qsphere/ε0 = 100π N m^2/C

Solving for Qsphere:

Qsphere = ε0*100π N m^2/C = (8.85*10^-12 C^2/N m^2)*(100π N m^2/C) = 2.8*10^-9 C = 2.8 nC

Now we can consider the effects of introducing charge Q at the center of the sphere. Since the sphere is a conductor, the charge will distribute itself uniformly across the surface of the sphere, and the electric field just outside the surface will still be directed outward. If we assume that this charge distribution does not significantly affect the radius of the sphere, then the electric field just outside the surface of the sphere will be:

E' = (1/4πε0)*Qsphere/(0.2 m)^2

We know from the problem that the new electric field is 100 N/C, so:

100 N/C = E' = (1/4πε0)*Qsphere/(0.2 m)^2

Solving for Q:

Q = E'*(0.2 m)^2*4πε0

Q ≈ 1.8 nC

Question 15

Which one of the following is not an expression for electric charge?

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Question 16

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.The charges on the inner and outer surfaces of the shell are respectively

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The answer of An uncharged spherical conducting shell surrounds a...

Question 17

The electric flux through the two adjacent spherical surfaces shown below is known to be the same. 
It is also known that there is no charge inside either spherical surface.We can conclude that

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Question 18

A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground.The outside of the sphere is then grounded as shown.Then the ground wire is removed.A is the inner surface and B is the outer surface.Which statement is correct?

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The answer of A positive point charge q is placed...

Question 19

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge −Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

Accepted Answer

The answer of Two concentric imaginary spherical surfaces of radius...

Question 20

A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown.Where is the induced charge density greatest in magnitude and what is its sign?

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The answer of A positive point charge q is placed...

Quiz 24: Gausss Law

Which one of the following cannot be a statement of Gauss's Law for some physical situation?

A constant electric field Is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm.The electric flux through the plane's surface,in N ⋅ m²/C,is

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

When a cube is inscribed in a sphere of radius r,the length L of a side of the cube is ) If a positive point charge Q is placed at the center of the spherical surface,the ratio of the electric flux Φ_sphere at the spherical surface to the flux Φ_cube at the surface of the cube is

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.

Three originally uncharged infinite parallel planes are arranged as shown.Then the upper plate has surface charge density σ placed on it while the lower plate receives surface charge density −σ.The net charge induced on the center plate is

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.Then charge +3q is placed on the outside of the shell.When static equilibrium is reached,the charges on the inner and outer surfaces of the shell are respectively

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?

An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station.Which statement is correct?

An uncharged metal sphere is placed on an insulating puck on a frictionless table.While being held parallel to the table,a rod with a charge q is brought close to the sphere,but does not touch it.As the rod is brought in,the sphere

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?

Which one of the following is not an expression for electric charge?

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.The charges on the inner and outer surfaces of the shell are respectively

The electric flux through the two adjacent spherical surfaces shown below is known to be the same. It is also known that there is no charge inside either spherical surface.We can conclude that

A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground.The outside of the sphere is then grounded as shown.Then the ground wire is removed.A is the inner surface and B is the outer surface.Which statement is correct?

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge −Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown.Where is the induced charge density greatest in magnitude and what is its sign?

Quiz 24: Gausss Law

Which one of the following cannot be a statement of Gauss's Law for some physical situation?

A constant electric field Is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm.The electric flux through the plane's surface,in N ⋅ m2/C,is

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces.When compared to the electric flux Φ1 through the surface of radius R,the electric flux Φ2 through the surface of radius 2R is

When a cube is inscribed in a sphere of radius r,the length L of a side of the cube is ) If a positive point charge Q is placed at the center of the spherical surface,the ratio of the electric flux Φsphere at the spherical surface to the flux Φcube at the surface of the cube is

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.

Three originally uncharged infinite parallel planes are arranged as shown.Then the upper plate has surface charge density σ placed on it while the lower plate receives surface charge density −σ.The net charge induced on the center plate is

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.Then charge +3q is placed on the outside of the shell.When static equilibrium is reached,the charges on the inner and outer surfaces of the shell are respectively

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?

An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station.Which statement is correct?

An uncharged metal sphere is placed on an insulating puck on a frictionless table.While being held parallel to the table,a rod with a charge q is brought close to the sphere,but does not touch it.As the rod is brought in,the sphere

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?

Which one of the following is not an expression for electric charge?

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.The charges on the inner and outer surfaces of the shell are respectively

The electric flux through the two adjacent spherical surfaces shown below is known to be the same. It is also known that there is no charge inside either spherical surface.We can conclude that

A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground.The outside of the sphere is then grounded as shown.Then the ground wire is removed.A is the inner surface and B is the outer surface.Which statement is correct?

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge −Q located at the center of the surfaces.When compared to the electric flux Φ1 through the surface of radius R,the electric flux Φ2 through the surface of radius 2R is

A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown.Where is the induced charge density greatest in magnitude and what is its sign?

A constant electric field Is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm.The electric flux through the plane's surface,in N ⋅ m²/C,is

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

When a cube is inscribed in a sphere of radius r,the length L of a side of the cube is ) If a positive point charge Q is placed at the center of the spherical surface,the ratio of the electric flux Φ_sphere at the spherical surface to the flux Φ_cube at the surface of the cube is

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge −Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is