Exam 24: Gausss Law

A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface. This is

A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of −3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.

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

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis?

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m³) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere.

A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies?

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

Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m² and −0.60 nC/m². What is the magnitude of the electric field at a point between the two surfaces?

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

Charge of uniform density (20 nC/m²) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of −12 nC/m². Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces.

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

A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m. If the magnitude of the electric flux through the surface at x = 2 m is 4 N ⋅ m²/C, what is the magnitude of the electric flux through the surface at x = 4 m?

The nucleus of a hydrogen atom, a proton, sets up an electric field. The distance between the proton and electron is about 5.1 × 10−¹¹ m. What is the magnitude of the electric field at this distance from the proton? [The charge on the proton is +1.6 × 10−¹⁹ C.]

Charge of uniform density (80 nC/m³) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis.

If we define the gravitational field , where is a unit radial vector, then Gauss's Law for gravity is

Charge of uniform density (0.30 nC/m²) is distributed over the xy plane, and charge of uniform density (−0.40 nC/m²) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes?

Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density ρ at constant velocity is for an imaginary surface within the fluid. Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid. Which one, if either, is correct?

A uniform electric field is present in the region between the infinite parallel planes of charge A and B, and a uniform electric field is present in the region between the infinite parallel planes of charge B and C. When the planes are vertical and the fields are both non-zero,

A uniform electric field is present in the region between infinite parallel plane plates A and B and a uniform electric field is present in the region between infinite parallel plane plates B and C. When the plates are vertical, is directed to the right and to the left. The signs of the charges on plates A, B and C may be

A spaceship encounters a single plane of charged particles, with the charge per unit area equal to σ. The electric field a short distance above the plane has magnitude ____ and is directed ____ to the plane.