1.2 Gauss's Law

Gauss's law provides a convenient way to calculate the electric field outside and near each of the following isolated charged conductors EXCEPT a:

Cube

A closed surface, in the shape of a cube of side a, is oriented as shown above in a region where there is a constant electric field of magnitude E parallel to the x-axis. The total electric flux through the cubical surface is:

Zero

The net electric flux through a closed surface is:

Zero if the net charge enclosed by the surface is zero

A charge +q is placed at the center of a tetrahedron whose faces are all equilateral triangles, as shown above. What is the flux of the electric field through one face of the tetrahedron?

q/(4E0)

Two concentric spherical surfaces are drawn around an isolated positive charge +q located at their center, as shown above. The inner surface has a radius that is ½ that of the outer surface. If the total electric flux passing through the inner surface is φ(phi), what is the total electric flux passing through the outer surface?

φ(phi)

A hollow metal sphere of radius R is positively charged. Of the following distances from the center of the sphere, which location will have the greatest electric field strength?

(5R)/4

The electric field of two long coaxial cylinders is represented by lines of force as shown above. The charge on the inner cylinder is +Q. The charge on the outer cylinder is:

-3Q

A small positive charge of magnitude +17.7 x 10-9 C is situated at the center of a Gaussian surface in the shape of a cube with sides 6 centimeters in length, as shown above. The permittivity of free space is 8.85 x 10-12 C^2/N∙m^2. What is the net flux through the cube?

2000 N∙m^2/C

A small positive charge of magnitude +17.7 x 10-9 C is situated at the center of a Gaussian surface in the shape of a cube with sides 6 centimeters in length, as shown above. The permittivity of free space is 8.85 x 10-12 C^2/N∙m^2. What is the net flux through the top surface?

333 N∙m^2/C

A conducting sphere of radius R carries a charge Q. Another conducting sphere has a radius R/2, but carries the same charge. The spheres are far apart. The ratio of the electric field near the surface of the smaller sphere to the field near the surface of the larger sphere is most nearly:

4

An electric field is produced by the very long, uniformly charged rod drawn above. If the strength of the electric field is E1 at a distance r1 from the axis of the rod, at what distance from the axis is the field strength E1/4?

4r1

A small positive charge of magnitude +17.7 x 10-9 C is situated at the center of a Gaussian surface in the shape of a cube with sides 6 centimeters in length, as shown above. The permittivity of free space is 8.85 x 10-12 C^2/N∙m^2. What is the magnitude of the electric field at any vertex of the cube?

5.9x10^4 N/C

The electric field E just outside the surface of a charged conductor is:

Directed perpendicular to the surface

A solid nonconducting sphere of radius R has a charge Q uniformly distributed throughout its volume. A Gaussian surface of radius r with r<R is used to calculate the magnitude of the electric field E at a distance r from the center of the sphere. Which of the following equations results from a correct application of Gauss's law for this situation?

E(4pir^2)=(Qr^3)/(E0R^3)

Two concentric spherical surfaces are drawn around an isolated positive charge +q located at their center, as shown above. The inner surface has a radius that is ½ that of the outer surface. If the electric field strength at the inner surface is E, what is the field strength at the outer surface?

E/4

The figure above shows a spherical distribution of charge of radius R and constant charge density p(rho). Which of the following graphs best represents the electric field strength E as a function of the distance r from the center of the sphere?

Graph C

Reasons why a Gaussian surface in the shape of a sphere would be a better choice than the cube shown include which of the following? I. The electric field lines would be parallel to the area normal for each and every element dA of the Gaussian surface. II. The electric field would be of uniform magnitude at the location of each and every element dA of the Gaussian surface. III. The magnitude of the electric field would be equal to 17.7 x 10-9 N/C at the location of each and every element dA of the Gaussian surface.

I and II only

The two charged metal spheres X and Y shown above are far apart, and each is isolated from all other charges. The radius of sphere X is greater than that of sphere Y, and the magnitudes of the electric fields just outside their surfaces are the same. How does the charge on sphere X compare with that on sphere Y ?

It is greater

A solid conducting sphere is given a positive charge Q. How is the charge Q distributed in or on the sphere?

It is uniformly distributed on the surface of the sphere only

Two concentric, spherical conducting shells have radii r1 and r2 and charges Q1 and Q2, as shown above. Let r be the distance from the center of the spheres and consider the region r1<r< r2. In this region the electric field is proportional to:

Q1/r^2