2. A cube with 1.4-m edges is oriented as shown... electric field. Find the electric flux through the right face... Homework #3 203-1-1721 ...

2. A cube with 1.4-m edges is oriented as shown... electric field. Find the electric flux through the right face... Homework #3 203-1-1721 ...

Homework #3
203-1-1721
Physics 2 for Students of Mechanical Engineering
Part A
2. A cube with 1.4-m edges is oriented as shown in Fig. 27-24 in a region of uniform
electric field. Find the electric flux through the right face if the electric field is given
by (a) (6 N/C)i (b) (-2 N/C)j and (c) (-3 N/C)i + (4 N/C) k. (d) Calculate the total
flux through the cube for each of these fields.
5. A point charge of 1.84 x 10-6 C is at the center of a cubical Gaussian surface with
edges that are 55 cm long. Fine the electric flux, ΦE, through the surface.
11. A point charge q is placed at one corner of a cube of edge a. What is the flux
through each of the cube faces? (Hint: Use Gauss's law and symmetry arguments.)
12. An infinite line of charge produces a field of 4.52 x 104 N/C at a distance of 1.96 m.
Calculate the linear charge density.
14. Two thin, large, nonconducting sheets of positive charge face each other as in Fig.
27-28. What is E at points (a) to the left of the sheets, (b) between them and (c) to
the right of the sheets? Assume the same surface charge density σ for each sheet.
Consider only points not near the edges whose distance from the sheets is small
compared to the dimensions of the sheets.
15. Two large metal plates face each other as in Fig. 27-29 and carry charges with
surface charge density +σ and -σ, respectively on their inner surfaces (why?). Find E
at points (a) to the left of the plates, (b) between them, and (c) to the right of the
plates. Consider only points not near the edges whose distance from the plates are
small compared to the dimensions of the plates.
17. A very long straight thin wire carries -3.60 x 10-9 C/m of fixed negative charge. The
wire is to be surrounded by a uniform cylinder of positive charge, radius 1.50 cm,
coaxial with the wire. The volume charge density ρ of the cylinder is to be selected
so that the net electric field outside the cylinder is zero. Calculate the required
positive charge density ρ.
Part B
3. A small sphere whose mass m is 1.12 mg carries a charge q = 19.7 x 10-9 C. It hangs
in Earth's gravitational field from a silk thread that makes an angle θ = 27.4° with a
large, uniformly charged, nonconducting sheet as in Fig. 27-32. Calculate the
uniform charge density σ for the sheet.
4. Figure 27-33 shows a charge +q arranged on a uniform conducting sphere of radius a
and placed at the center of a spherical conducting shell of inner radius b and outer
radius c. The outer shell carries a charge of –q. Find E(r) at locations (a) within the
sphere (r < a), (b) between the sphere and the shell (a < r < b), (c) inside the shell (b
< r < c), and (d) outside the shell (r > c). (e) What charges appear on the inner and
outer surfaces of the shell?
6. A large, flat, nonconducting surface carries a uniform charge density σ. A small
circular hole of radius R has been cut in the middle of the sheet, as shown in Fig. 2735. Ignore fringing of the field lines around all edges and calculate the electric field
a point P, a distance z from the center of the hole along its axis.