Charge and Flux

1.  A positive point charge q is at the center of a cube side L. A large number N of electric field lines are drawn from the point charge.

a.  How many of the field lines pass through the surface of the cube?

b.  How many lines pass through each face, assuming none pass through the corners and edges?

c.  What is the net outward flux of the electric field through the cubic surface?

d.  What is the flux of the electric field through one face of the cube?

2.  A thick, non-conducting spherical shell of inner radius a and outer radius b has a uniform volume density p. Find the total charge and electric field (in terms of p):

a.  when r<a

b.  when a<r<b

c.  when r>b

3.  An infinitely long concentric cable has inner conductor of diameter 3 cm and has a linear charge density of 6E-9 C/m while the outer conductor of inner diameter 6cm and outer diameter of 13 cm, is uncharged.

a.  Find the electric field for all values of r (in terms of r).

b.  What are the surface charge densities on the inner and outer surface of the outer conductor?

4.  Consider 3 concentric metal spheres. The inner sphere (sphere I) is a solid sphere with radius R1. Sphere II, which is hollow (and next in line) has inner radius R2 and outer radius R3. Sphere III is also a hollow sphere, around sphere II with inner radius R4 and outer radius R5. Initially, all three spheres have zero excess charge. Then a negative charge –Q is placed on sphere I and a positive charge +Q is placed on sphere III.

a.  After the charges reach equilibrium, which direction will the electric field in the space between spheres I and II point, if at all?

b.  How much charge will be on the inner surface of sphere II?

c.  How much charge will be on the outer surface of sphere II?

d.  How much charge will be on the inner surface of sphere III?

e.  How much charge will be on the outer surface of sphere III?

5.  A spherical conducting shell with zero net charge has an inner radius a and an outer radius b. A point charge q is placed at the center of the shell. Find the electric field:

a. when r<a

b. when a<r<b

c.  when r>b

d.  Draw the field lines for this situation.