Physics 112 HW3
DUE Wednesday, 11 September 2013
U2-EP01. Three charges lie on the x-axis. The one at x = 0 has charge –q, the one at x = 1 cm has
charge +2q, and the one at x = 2 cm has charge –q. Sketch the electric field lines in the x-y
plane.
U2-EP02. Repeat #1 above, except now the charge at x = 1 cm has charge +3q.
U2-EP03. Two equal positive charges +q are on the y-axis. One is at y = a and the other is at y =
–a.
a) Sketch the electric field lines in the x-y plane.
b) Derive an expression for the electric field at points on the y-axis for y>a.
c) Derive an expression for the electric field at points on the x-axis.
d) Using your result from part c, show that for x >> a, the magnitude of the electric field is
approximately 2kq/x2. Explain why you would expect this result even before calculating
it.
U2-EP04. Now we have a +q charge on the y-axis at y = a, and a –q charge at y = –a.
a) Sketch the electric field lines in the x-y plane.
b) Derive an expressions for the electric field at points on the y-axis for y>a and –a<y<a.
c) Derive an expression for the electric field at points on the x-axis.
d) Using your result from part c, show that for x >> a the magnitude of the electric field is
approximately 2kqa/x3. This arrangement is called an electric dipole.
U2-EP05. Three charges are in the x-y plane: a +1 μC charge is at (x,y) = (0 cm, 2 cm), a +2 μC
charge is at (0 cm, 0 cm), and another +1 μC charge is at (2 cm, 0 cm).
a) Find the magnitude of the electric field at the point halfway between the two +1 μC
charges.
b) Will your answer to part a) change if we replace the two +1 μC charges with –1 μC
charges? Why or why not?
c) Will your answer to part a) change if we get rid of the two +1 μC charges completely?
Why or why not?
U2-ECa01. An electron travels to the right at a speed of 106 m/s. It suddenly enters the space
between two large parallel plates that are 2 cm apart. The plates are charged in such a way that
the electric field between them is uniform. It has a value of 50 N/C and it points up (see
diagram). If the electron enters the region between the plates exactly halfway between them,
where will it hit a plate? And which plate will it hit—the upper one or the lower one?
electron
106 m/s
E
2 cm