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Exam 22: Gausss Law

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Question 21

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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.

A) 5.52 × 10⁵ Nm²/C
B) 1.13 × 10⁵ Nm²/C
C) 2.26 × 10⁵ Nm²/C
D) 0.565 × 10⁵ Nm²/C
E) 0

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Question 22

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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) 6 Nm²/C
B) 0
C) 24 Nm²/C
D) 12 Nm²/C
E) 48 Nm²/C

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Question 23

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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?

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

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

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

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

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?

If the electric flux through a rectangular area is 5.0 N m²/C, and the electric field is then doubled, what is the resulting flux through the area?

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

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

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

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

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?

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?

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?

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

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

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?