PHYS 1404-004 Homework 3 – 02/11/2016
Due February 18th, 2016
Homework should be written out neatly on a separate sheet of paper. Explain your
reasoning.
1) A large negatively charged metal plate is lying horizontally, as in the picture
below. A positively charged conducting ball is located, as shown, above the plate.
Points A and B are points in space, not charges.
Draw possible electric field lines. Explain why you drew the field lines the way
you did. Is the field stronger, at point A or point B? Explain your reasoning.
2) The diagram below shows the region in the neighborhood of a large positively
charged conducting plate (extending far beyond the region shown) and a
negatively charged conducting sphere. Lines labeled A-F are shown and are said
to be the field lines for the electric field between the two charged objects.
a. Examine each one of the field lines and indicate whether it is a correctly
drawn field line. If any line is not correct in some way, explain what is
incorrect about it.
b. Redraw the diagram to make the pattern of field lines more nearly correct.
3) Consider a negatively charged particle entering a region between two charged
plates, as shown in the diagram below. The initial velocity of the particle is 7.0 ×
107 𝑚𝑚⁄𝑠𝑠. The mass of the particle is 9.1 × 10−31 𝑘𝑘𝑘𝑘 and the charge is −1.6 ×
10−19 𝐶𝐶. The distance between the plates is 0.025 𝑚𝑚. You can consider the
electrical force to be the only force acting between the plates. (The force of
gravity is negligible and can be considered to be zero in this problem.) The
electric field between the plates is such that the particle just reaches the negative
plate (the velocity at the negative plate is zero).
a. Determine the magnitude and the direction of the electric field. Show your
work and explain your reasoning.
b. Determine the potential difference between the plates. Show your work
and explain your reasoning.
c. Which plate is at a higher potential. Show your work and explain your
reasoning.
4) The figure below shows a positive charge 𝑞𝑞 which is being moved within a
uniform electric field 𝐸𝐸�⃑ from point 1 to point 2 along three different paths: a), b),
and c). How does the potential difference (∆𝑉𝑉) compare between all three paths?
How does the work required to move the particle compare between all three
paths? Explain your reasoning.
5) In the figure, 𝑞𝑞1 = +𝑞𝑞, 𝑞𝑞2 = −2𝑞𝑞, 𝑞𝑞3 = −𝑞𝑞, and 𝑞𝑞4 = +2𝑞𝑞. What is the
electric field at the center of the square if 𝑞𝑞 = 1.0 × 10−8 𝐶𝐶 and the distance
between charge centers 𝑎𝑎 = 5.0 𝑐𝑐𝑐𝑐.
6) A uniform electric field exists in a region between two oppositely charged plates.
An electron is released from rest at the surface of the negatively charged plate and
strikes the surface of the opposite plate, 2.0 𝑐𝑐𝑐𝑐 away, in a time 1.5 × 10−8 𝑠𝑠.
a. What is the speed of the electron as it strikes the second plate?
b. What is the magnitude of the electric field 𝐸𝐸�⃑ ?
7) A small, plastic sphere of mass 𝑚𝑚 = 100 𝑔𝑔 is attached to a string
as shown in the figure. There is an electric field 𝐸𝐸�⃑ = 100 𝑁𝑁⁄𝐶𝐶 𝚤𝚤̂.
If the string makes an angle 𝜃𝜃 = 30° with the y-axis, what is the
charge on the sphere?