Physics222: Chapter 22*PRACTICE

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?

0

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

1.9 × 104 N m2/C

If the electric flux through a rectangular area is 5.0 Nm2/C, and the electric field is then doubled, what is the resulting flux through the area?

10 Nm2/C

An infinitely long cylinder of radius R = 2 cm carries a uniform charge density = 18 μC/m3. Calculate the electric field at distance r = 1 cm from the axis of the cylinder.

10.2 × 103 N/C

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.

2.26 × 105 N m2/C

A spherical, non-conducting shell of inner radius r1= 10 cm and outer radius r2= 15 cm carries a total charge Q = 15 μC distributed uniformly throughout its volume. What is the electric field at a distance r= 12 cm from the center of the shell?

2.87 × 106 N/C

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?

20 Nm2/C

Two parallel flat planes of positive charge are separated by a distance d. Plane #1 has charge density and plane #2 has a charge density 2. 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

a) fields will point opposite directions so E total = E1 - E2 = sigma1/2 e0 - sigma/2e0 = (sigma1 - sigma2)/(2 e0) b) now they add since they will point the same way Etotal = (sigma1 + sigma2)/(2 e0)

Outside a spherically symmetric charge distribution of net charge Q, Gauss's law can be used to show that the electric field at a given distance

acts like it is formed by a point charge Q at the center of the distribution

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

along a line between the lines closer to line #2 than line #1

A region of space contains a uniform electric field oriented along the y-axis. A frame of surface area A is placed perpendicular to the y-axis in the xz-plane. The magnitude of the electric flux through this frame is 0. A second frame is placed in the same electric field in such a way that the magnitude of the electric flux through it is 0/2. How is the plane of second frame oriented with respect to the plane of the first one?

at a 60° angle

Gaussian surfaces A and B enclose the same positive charge +Q. The area of Gaussian surface A is three times larger than that of Gaussian surface B. The flux of electric field through Gaussian surface A is

equal to the flux of electric field through Gaussian surface B.

An advantage in evaluating surface integrals related to Gauss's law for symmetric charge distributions is

the electric field is of constant magnitude on certain surfaces.

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?

the electric field isE = E1i + E2j where E1 and E2 are positive constants the net electric field isE = (E1^2 + E2^2)^1/2 the electric flux through the frame isO_e = E * A where A is surface are of cube and has value 6a^2 or O_e = E * 6a^2 = 6E * a^2

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

the volume charge density in the sphere is = total charge / total volume p = Q / (4/3)* pie * r^3 then the surface charge density = total charge / area p = Q / 4 * pie * r^2

A uniform electric field = E0 is set-up in a region of space. A frame is placed in that region in such a way that its plane is perpendicular to the y-axis. Which of the following changes would decrease the magnitude of the electric flux through the frame?

tilting the frame so that its plane is now in the yz-plane

A charge QQ is positioned at the center of a sphere of radius RR. The flux of the electric field through the sphere is equal to ΦΦ. If the charge QQ is now placed at the center of a cube the flux of the electric field through the surface of the cube is equal to

Φ

If a charge is located at the center of a spherical volume and the electric flux through the surface of the sphere is Φ0Φ0, what is the flux through the surface if the radius of the sphere doubles?

Φ0

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

σ/ε

A non-conducting sphere of radius R = 7 cm carries a charge Q = 4 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?

3.5 cm and 9.9 cm

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?

30 Nm2/C

The electric field in a region of space is oriented along the positive y axis. A circle of radius R is placed in the xz-plane. The flux of the electric field through this circle is . The same electric field passing through a second circle of radius 2R parallel to xz-plane would result in a flux equal to

4

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?

6 × 10^4 Nm2/C

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?

60%

If a rectangular area is rotated in a uniform electric field from the position where the maximum electric flux goes through it to an orientation where only half the flux goes through it, what has been the angle of rotation?

60°

Fig. 22-1 shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have an electric flux of +q/εo through them?

B

Fig. 22-1 shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them?

C

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?

E =Q/EoL^2

A solid non-conducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a radius r (r < R) from the center of the sphere the electric field has a value E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R the magnitude of the electric field at a radius r would be equal to

E/8.

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?

E0

A solid non-conducting sphere of radius R carries a charge Q1 distributed uniformly. The sphere

E= 1/4piEo(Q2/r^2)

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?

E=KQ/2R^2

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

Enet=(x1-x2)/pi*a*Eo

Gauss's law can be applied using any surface.

False

Gauss's law may be applied only to charge distributions that are symmetric.

False

If the net flux through a closed surface is zero, then there can be no charge or charges within that surface.

False

State Gauss's law.

Gauss's law states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge

Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. Where should the charge be located to maximize the magnitude of the flux of the electric field through the Gaussian surface?

The flux does not depend on the position of the charge as long as it is inside the sphere

A positive charge QQ is located at the center of an imaginary Gaussian cube of sides aa. The flux of the electric field through the surface of the cube is ΦΦ. A second, negative charge −Q−Q is placed next to QQ inside the cube. Which of the following statements will be true in this case?

The net flux through the surface of the cube is equal to zero

If a closed surface surrounds a dipole, the net flux through the surface is zero.

True

If the net flux through a closed surface is positive, then the net charge enclosed must be positive

True

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

24 Nm2/C