Question 1

As shown in the figure,a square insulating slab 5.0 mm thick measuring  has a charge of  distributed uniformly throughout its volume.Use Gauss's law to determine the electric field at point P,which is located within the slab beneath its center,1.0 mm from one of the faces.

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Question 2

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume.At what distance,measured from the center of the sphere,does the electric field reach a value equal to half its maximum value?

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Question 3

A spherical,non-conducting shell of inner radius  = 10 cm and outer radius  = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell.What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell?

Accepted Answer

Since the charge is uniformly distributed on the shell, at any point inside the shell, the electric field is zero. At a distance r=12 cm, the point is inside the shell, so the electric field at that point is zero. Therefore, the correct answer is B). However, if the point is outside the shell, the electric field can be found using Coulomb's law, which is E=kQ/r^2, where k is Coulomb's constant, Q is the total charge on the shell, and r is the distance from the center of the shell. In this case, r=12 cm, so the electric field is E=kQ/r^2=9x10^9 Nm^2/C^2 x 15x10^-6 C/(0.12 m)^2 = 2.87x10^4 N/C = C).

Question 4

Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other.The upper sheet carries  .The electric field midway between the sheets is  pointing downward.What is the surface charge density on the lower sheet?

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Question 5

Electric charge is uniformly distributed inside a nonconducting sphere of radius  .The electric field at a point P,which is 0.50 m from the center of the sphere,is  and is directed radially outward.What is the maximum magnitude of the electric field due to this sphere?

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Question 6

A very large sheet of a conductor carries a uniform charge density of  on its surfaces.What is the electric field strength 3.00 mm outside the surface of the conductor?

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Question 7

The cross section of a long coaxial cable is shown in the figure,with radii as given.The linear charge density on the inner conductor is  and the linear charge density on the outer conductor is  The inner and outer cylindrical surfaces are respectively denoted by A,B,C,and D,as shown.  The radial component of the electric field at a point that 34 mm from the axis is closest to

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Question 8

The cross section of a long coaxial cable is shown in the figure,with radii as given.The linear charge density on the inner conductor is  and the linear charge density on the outer conductor is  The inner and outer cylindrical surfaces are respectively denoted by A,B,C,and D,as shown.  The magnitude of the electric field at a point that is  from the axis is closest to

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Question 9

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a  point charge placed at its center.Find the surface charge density
(a)on the inner surface of the shell.
(b)on the outer surface of the shell.

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Question 10

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume.At a certain distance r₁ (r₁ < R)from the center of the sphere,the electric field has magnitude E.If the same charge Q were distributed uniformly throughout a sphere of radius 2R,the magnitude of the electric field at the same distance r₁ from the center would be equal to

Accepted Answer

From Gauss's Law, we know that the electric field at a distance r from the center of a uniformly charged sphere of radius R and total charge Q is given by:

E = K * Q * r / R^3

where K = 1 / (4πε0) is the Coulomb constant and ε0 is the permittivity of free space.

If we take the ratio of the electric field at distance r from the center of a sphere of radius R with charge Q to the electric field at distance r from the center of a sphere of radius 2R with charge Q, we get:

E(R) / E(2R) = (K * Q * r / R^3) / (K * Q * r / (2R)^3)
              = 1 / 8

Therefore, the magnitude of the electric field at distance r from the center in the second case is:

E'(r) = E(r) / 8
      = E / 8

So the answer is A) E/8.

Question 11

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center.  =  The radial component of the electric field at a point that is 1.50 m from the center is closest to

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Question 12

Electric charge is uniformly distributed inside a nonconducting sphere of radius  .The electric field at a point P,which is 0.50 m from the center of the sphere,is  and is directed radially outward.At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

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Question 13

Charge is distributed uniformly throughout a large insulating cylinder of radius R.The charge per unit length in the cylindrical volume is λ. (a)Use Gauss's law to find the magnitude of the electric field at a distance r from the central axis of the cylinder for r < R.Your answer should be in terms of r,R,λ,ε₀,and π. (b)Check the reasonableness of your answer by evaluating it at the surface of the cylinder.

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Question 14

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance from the center,the electric field has a magnitude E₀.What is the magnitude of the electric field at a radial distance ?

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Question 15

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of  Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder.

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Question 16

A huge (essentially infinite)horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces.The upper face carries  while the lower face carries  .What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face?

Accepted Answer

By Gauss's law, the electric field inside a uniformly charged infinite sheet is given by:

$E = \frac{\sigma}{2\epsilon_0}$

Where $\sigma$ is the surface charge density and $\epsilon_0$ is the permittivity of free space.

Since the sheet has charge on both sides, the net surface charge density is:

$\sigma_{net} = \sigma_{top} - \sigma_{bottom}$

Substituting the given values, we get:

$\sigma_{net} = 11.0 \mu C / m^2 - (-11.0 \mu C / m^2) = 22.0 \mu C / m^2$

Now, we can use the formula for the electric field:

$E = \frac{\sigma_{net}}{2\epsilon_0} = \frac{22.0 	imes 10^{-6} C/m^2}{2 	imes 8.85 	imes 10^{-12} C^2/Nm^2} = 6.78 	imes 10^{10} N/C$

Since the point of interest is 2 cm below the upper face, we can conclude that the electric field at that point is equal to the electric field inside the sheet, which is given by the formula above.

Therefore, the correct answer is C) 6.78 × 10^10 N/C.

Question 17

A nonconducting spherical shell of inner radius R₁ and outer radius R₂ contains a uniform volume charge density ρ throughout the shell.Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere.Your answers should be in terms of ρ,R₁,R₂,r,ε₀,and π. (a)r < R₁ (b)R₁ < r < R₂ (c)r > R₂

Accepted Answer

The answer of A nonconducting spherical shell of inner radius...

Question 18

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries an excess charge of  .A point charge of  is present at the center.The surface charge density on the inner spherical surface is closest to

Accepted Answer

Since the charge is located at the center of the shell, it will induce charges on both inner and outer surfaces of the shell. Since the shell is conducting, the charges will distribute themselves in a way such that there is no electric field inside the shell. This means that the charge on the inner surface of the shell must be equal in magnitude and opposite in sign to the point charge at the center.

Therefore, the surface charge density on the inner surface of the shell can be found using the formula: sigma = Q/A, where Q is the charge on the surface and A is the surface area.

The surface area of the inner surface can be found using the formula for the surface area of a sphere: A = 4πr^2.

Therefore, sigma = (-11.8 nC) / (4π(0.8 m)^2) = -4.07 × 10^-8 C/m^2

The closest answer choice is D, -4.0 × 10^-8 C/m^2.

Question 19

Consider two closely spaced and oppositely charged parallel metal plates.The plates are square with sides of length L and carry charges Q and -Q on their facing surfaces.What is the magnitude of the electric field in the region between the plates?

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Question 20

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center.  =  The radial component of the electric field at a point that is 0.60 m from the center is closest to

Accepted Answer

Since the point charge is at the center of the sphere, it will not affect the radial component of the electric field at a point that is at a distance of 0.60 m from the center. Therefore, we only need to consider the electric field due to the net excess charge on the spherical shell.

The electric field due to a uniformly charged spherical shell with a net charge Q and radius R at a point outside the shell is given by:

E = k(Q/R^2)

where k is the Coulomb constant.

At a distance of 0.60 m from the center of the sphere, the radial distance from the center of the spherical shell is 0.60 - 0.80 = 0.20 m. Therefore, the electric field at this point is:

E = k(Q/R^2) = (9 x 10^9 N*m^2/C^2)(-500 x 10^-9 C)/(0.8 m)^2 = -7500 N/C

The negative sign indicates that the electric field points inward, towards the center of the spherical shell. Therefore, the best choice is C: -7500 N/C.

Quiz 22: Gausss Law

As shown in the figure,a square insulating slab 5.0 mm thick measuring has a charge of distributed uniformly throughout its volume.Use Gauss's law to determine the electric field at point P,which is located within the slab beneath its center,1.0 mm from one of the faces.

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume.At what distance,measured from the center of the sphere,does the electric field reach a value equal to half its maximum value?

A spherical,non-conducting shell of inner radius = 10 cm and outer radius = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell.What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell?

Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other.The upper sheet carries .The electric field midway between the sheets is pointing downward.What is the surface charge density on the lower sheet?

Electric charge is uniformly distributed inside a nonconducting sphere of radius .The electric field at a point P,which is 0.50 m from the center of the sphere,is and is directed radially outward.What is the maximum magnitude of the electric field due to this sphere?

A very large sheet of a conductor carries a uniform charge density of on its surfaces.What is the electric field strength 3.00 mm outside the surface of the conductor?

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a point charge placed at its center.Find the surface charge density (a)on the inner surface of the shell. (b)on the outer surface of the shell.

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center. = The radial component of the electric field at a point that is 1.50 m from the center is closest to

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance from the center,the electric field has a magnitude E₀.What is the magnitude of the electric field at a radial distance ?

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder.

A huge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces.The upper face carries while the lower face carries .What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face?

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries an excess charge of .A point charge of is present at the center.The surface charge density on the inner spherical surface is closest to

Consider two closely spaced and oppositely charged parallel metal plates.The plates are square with sides of length L and carry charges Q and -Q on their facing surfaces.What is the magnitude of the electric field in the region between the plates?

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center. = The radial component of the electric field at a point that is 0.60 m from the center is closest to

Quiz 22: Gausss Law

As shown in the figure,a square insulating slab 5.0 mm thick measuring has a charge of distributed uniformly throughout its volume.Use Gauss's law to determine the electric field at point P,which is located within the slab beneath its center,1.0 mm from one of the faces.

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume.At what distance,measured from the center of the sphere,does the electric field reach a value equal to half its maximum value?

A spherical,non-conducting shell of inner radius = 10 cm and outer radius = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell.What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell?

Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other.The upper sheet carries .The electric field midway between the sheets is pointing downward.What is the surface charge density on the lower sheet?

Electric charge is uniformly distributed inside a nonconducting sphere of radius .The electric field at a point P,which is 0.50 m from the center of the sphere,is and is directed radially outward.What is the maximum magnitude of the electric field due to this sphere?

A very large sheet of a conductor carries a uniform charge density of on its surfaces.What is the electric field strength 3.00 mm outside the surface of the conductor?

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a point charge placed at its center.Find the surface charge density (a)on the inner surface of the shell. (b)on the outer surface of the shell.

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center. = The radial component of the electric field at a point that is 1.50 m from the center is closest to

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance from the center,the electric field has a magnitude E0.What is the magnitude of the electric field at a radial distance ?

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder.

A huge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces.The upper face carries while the lower face carries .What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face?

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries an excess charge of .A point charge of is present at the center.The surface charge density on the inner spherical surface is closest to

Consider two closely spaced and oppositely charged parallel metal plates.The plates are square with sides of length L and carry charges Q and -Q on their facing surfaces.What is the magnitude of the electric field in the region between the plates?

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center. = The radial component of the electric field at a point that is 0.60 m from the center is closest to

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance from the center,the electric field has a magnitude E₀.What is the magnitude of the electric field at a radial distance ?