Question 1

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2 respectively. λ1 > λ2. The electric field halfway between the lines, which are separated by a distance a, has magnitude

Accepted Answer

The answer of Two long straight parallel lines of charge,...

Question 2

A charge q = 2 μC is placed at the origin in a region where there is already a uniform electric field  = (100 N/C)  . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10 cm centered at the origin.

Accepted Answer

The answer of A charge q = 2 μC is...

Question 3

A solid non-conducting sphere of radius R carries a charge Q₁ distributed uniformly. The sphere is surrounded by a concentric spherical shell of inner radius R_a and outer radius R_b. The shell carries a total charge Q₂ distributed uniformly in its volume. What is the net electric field at a radial distance r such that R < r < R_a?

Accepted Answer

The answer of A solid non-conducting sphere of radius R...

Question 4

Consider two oppositely charged, parallel metal plates. The plates are square with sides L and carry charges Q and -Q. What is the magnitude of the electric field in the region between the plates?

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The answer of Consider two oppositely charged, parallel metal plates....

Question 5

A long straight line of charge has a uniform positive charge per unit length λ. The line is partially enclosed in a long rectangular box of length L and ends of area A, the line running through the center of each end. The electric flux through the surface of the box is

Accepted Answer

The answer of A long straight line of charge has...

Question 6

If the electric flux through a circular area is 5.0 Nm²/C, what is the electric flux through a circle of double the diameter assuming the orientations of the circles are the same and the electric field is uniform?

Accepted Answer

The electric flux through a circle is proportional to the area of the circle. If the diameter of the circle is doubled, the area of the circle is quadrupled. Therefore, the electric flux through the circle of double the diameter is four times the electric flux through the original circle.

Question 7

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The maximum magnitude of the electric field in the vicinity of the planes is

Accepted Answer

The answer of Three parallel flat planes of charge are...

Question 8

Consider an electric field  = 2x  - 3y  . The coordinates x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x, y, z) = (0, 2, 0), (2, 2, 0), (0, 2, 2)?

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Question 9

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r₁ = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r₂ = 2R?

Accepted Answer

The electric field inside a uniformly charged sphere is zero.

Question 10

A point charge q = +1 μC is located at the origin. What is the flux of the electric field of this charge through a square whose corners are (x, y, z) = (1, 1, 1), (-1, 1, 1), (-1, 1, -1), and (1, 1, -1)?

Accepted Answer

The answer of A point charge q = +1 μC...

Question 11

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. The charge density in the sphere is

Accepted Answer

The answer of A charge Q is uniformly distributed throughout...

Question 12

A region of space contains an electric field = E₁ + E₂ where E₁ and E₂ are positive constants. A frame whose corners are located at (x, y, z) = (a/2, 0, a/2), (-a/2, 0,-a/2), (a/2, 0,-a/2), and (-a/2, 0, a/2). What is the magnitude of the electric flux through the frame?

Accepted Answer

The answer of A region of space contains an electric...

Question 13

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R.
(a) What is the magnitude of the electric field at a distance R/2 from the center of the sphere?
(b) What is the magnitude of the electric field at a distance 2R from the center of the sphere?

Accepted Answer

The answer of A charge Q is uniformly distributed throughout...

Question 14

FIGURE 22-2 -A uniform electric field with a magnitude of 6 × 10⁶ N/C is applied to a cube of edge length 0.1 m as shown in Fig. 22-2. If the direction of the E-field is along the +x-axis, what is the electric flux passing through the shaded face of the cube?

Accepted Answer

The answer of FIGURE 22-2 
-A uniform electric field with...

Question 15

If a point charge is located at the center of a cylinder and the electric flux leaving one end of the cylinder is 20% of the total flux leaving the cylinder, what portion of the flux leaves the curved surface of the cylinder?

Accepted Answer

The answer of If a point charge is located at...

Question 16

If a point charge is located at the center of a cube and the electric flux through one face of the cube is 5.0 Nm²/C, what is the total flux leaving the cube?

Accepted Answer

The answer of If a point charge is located at...

Question 17

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The field in the regions between the planes has magnitude

Accepted Answer

The answer of Three parallel flat planes of charge are...

Question 18

Two parallel flat planes of positive charge are separated by a distance d. Plane #1 has charge density σ₁ and plane #2 has a charge density σ2. σ1> σ2. (a) In the region between the planes, the magnitude of the electric field is (b) In the region outside the planes the magnitude of the electric field is

Accepted Answer

The answer of Two parallel flat planes of positive charge...

Question 19

FIGURE 22-2 -An uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the flux of this field through a square of surface area A = 2 m²oriented parallel to the yz-plane?

Accepted Answer

The electric flux through a surface is given by the dot product of the electric field and the area vector. Since the square is parallel to the yz-plane, its area vector is along the x-axis. The electric field is along the y-axis, so the dot product is zero, resulting in zero flux.

Question 20

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2, respectively. λ1 > λ2. The locus of points where the electric field is zero in this case is

Accepted Answer

The electric field is zero at a point where the electric fields due to the two lines cancel each other out. This occurs along a line between the lines closer to line #2 than line #1, because the electric field due to line #1 is stronger than the electric field due to line #2.

Quiz 22: Gausss Law

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2 respectively. λ1 > λ2. The electric field halfway between the lines, which are separated by a distance a, has magnitude

A charge q = 2 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10 cm centered at the origin.

Consider two oppositely charged, parallel metal plates. The plates are square with sides L and carry charges Q and -Q. What is the magnitude of the electric field in the region between the plates?

A long straight line of charge has a uniform positive charge per unit length λ. The line is partially enclosed in a long rectangular box of length L and ends of area A, the line running through the center of each end. The electric flux through the surface of the box is

If the electric flux through a circular area is 5.0 Nm²/C, what is the electric flux through a circle of double the diameter assuming the orientations of the circles are the same and the electric field is uniform?

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The maximum magnitude of the electric field in the vicinity of the planes is

Consider an electric field = 2x - 3y . The coordinates x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x, y, z) = (0, 2, 0) , (2, 2, 0) , (0, 2, 2) ?

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r₁ = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r₂ = 2R?

A point charge q = +1 μC is located at the origin. What is the flux of the electric field of this charge through a square whose corners are (x, y, z) = (1, 1, 1) , (-1, 1, 1) , (-1, 1, -1) , and (1, 1, -1) ?

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. The charge density in the sphere is

A region of space contains an electric field = E₁ + E₂ where E₁ and E₂ are positive constants. A frame whose corners are located at (x, y, z) = (a/2, 0, a/2), (-a/2, 0,-a/2), (a/2, 0,-a/2), and (-a/2, 0, a/2). What is the magnitude of the electric flux through the frame?

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. (a) What is the magnitude of the electric field at a distance R/2 from the center of the sphere? (b) What is the magnitude of the electric field at a distance 2R from the center of the sphere?

FIGURE 22-2 -A uniform electric field with a magnitude of 6 × 10⁶ N/C is applied to a cube of edge length 0.1 m as shown in Fig. 22-2. If the direction of the E-field is along the +x-axis, what is the electric flux passing through the shaded face of the cube?

If a point charge is located at the center of a cylinder and the electric flux leaving one end of the cylinder is 20% of the total flux leaving the cylinder, what portion of the flux leaves the curved surface of the cylinder?

If a point charge is located at the center of a cube and the electric flux through one face of the cube is 5.0 Nm²/C, what is the total flux leaving the cube?

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The field in the regions between the planes has magnitude

FIGURE 22-2 -An uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the flux of this field through a square of surface area A = 2 m²oriented parallel to the yz-plane?

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2, respectively. λ1 > λ2. The locus of points where the electric field is zero in this case is

Quiz 22: Gausss Law

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2 respectively. λ1 > λ2. The electric field halfway between the lines, which are separated by a distance a, has magnitude

A charge q = 2 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10 cm centered at the origin.

Consider two oppositely charged, parallel metal plates. The plates are square with sides L and carry charges Q and -Q. What is the magnitude of the electric field in the region between the plates?

A long straight line of charge has a uniform positive charge per unit length λ. The line is partially enclosed in a long rectangular box of length L and ends of area A, the line running through the center of each end. The electric flux through the surface of the box is

If the electric flux through a circular area is 5.0 Nm2/C, what is the electric flux through a circle of double the diameter assuming the orientations of the circles are the same and the electric field is uniform?

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The maximum magnitude of the electric field in the vicinity of the planes is

Consider an electric field = 2x - 3y . The coordinates x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x, y, z) = (0, 2, 0) , (2, 2, 0) , (0, 2, 2) ?

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r1 = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

A point charge q = +1 μC is located at the origin. What is the flux of the electric field of this charge through a square whose corners are (x, y, z) = (1, 1, 1) , (-1, 1, 1) , (-1, 1, -1) , and (1, 1, -1) ?

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. The charge density in the sphere is

A region of space contains an electric field = E1 + E2 where E1 and E2 are positive constants. A frame whose corners are located at (x, y, z) = (a/2, 0, a/2), (-a/2, 0,-a/2), (a/2, 0,-a/2), and (-a/2, 0, a/2). What is the magnitude of the electric flux through the frame?

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. (a) What is the magnitude of the electric field at a distance R/2 from the center of the sphere? (b) What is the magnitude of the electric field at a distance 2R from the center of the sphere?

FIGURE 22-2 -A uniform electric field with a magnitude of 6 × 106 N/C is applied to a cube of edge length 0.1 m as shown in Fig. 22-2. If the direction of the E-field is along the +x-axis, what is the electric flux passing through the shaded face of the cube?

If a point charge is located at the center of a cylinder and the electric flux leaving one end of the cylinder is 20% of the total flux leaving the cylinder, what portion of the flux leaves the curved surface of the cylinder?

If a point charge is located at the center of a cube and the electric flux through one face of the cube is 5.0 Nm2/C, what is the total flux leaving the cube?

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The field in the regions between the planes has magnitude

FIGURE 22-2 -An uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the flux of this field through a square of surface area A = 2 m2 oriented parallel to the yz-plane?

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2, respectively. λ1 > λ2. The locus of points where the electric field is zero in this case is

If the electric flux through a circular area is 5.0 Nm²/C, what is the electric flux through a circle of double the diameter assuming the orientations of the circles are the same and the electric field is uniform?

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r₁ = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r₂ = 2R?

A region of space contains an electric field = E₁ + E₂ where E₁ and E₂ are positive constants. A frame whose corners are located at (x, y, z) = (a/2, 0, a/2), (-a/2, 0,-a/2), (a/2, 0,-a/2), and (-a/2, 0, a/2). What is the magnitude of the electric flux through the frame?

FIGURE 22-2 -A uniform electric field with a magnitude of 6 × 10⁶ N/C is applied to a cube of edge length 0.1 m as shown in Fig. 22-2. If the direction of the E-field is along the +x-axis, what is the electric flux passing through the shaded face of the cube?

If a point charge is located at the center of a cube and the electric flux through one face of the cube is 5.0 Nm²/C, what is the total flux leaving the cube?

FIGURE 22-2 -An uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the flux of this field through a square of surface area A = 2 m²oriented parallel to the yz-plane?