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Chapter 23
The Electric Field
Objectives
1. Electric fields
A. To understand the definition and utility of E-fields
B. To understand how to calculate E-fields for one point charge and several point charges.
E 

i
k qi
rˆ
ri 2
C. To understand how to calculate E-fields for continuous charge distributions.
E  k
rˆ dq
r2
(1) Line of charge
dq =  dl
 = charge/length
dl = small length
(2) Surface charge
dq =  dA
 = charge/area
dA = small area
2. Charge in an E-field
A. To understand the effect of an E-field on a point charge.
F  qE
F  ma
B. To understand the effect of an E-field on a dipole.
  p  E
U  p E
Chapter 23 problems
1.
What is the magnitude of the force on a 2.0 C charge in an electric field of 100 N/C?
2.
Two charges +q and one charge -q are located at the vertices of an equilateral triangle.
Sketch the electric field lines associated with this configuration.
3.
Two charges of +q are located at the vertices of an equilateral triangle as shown. What is
the E-field at the third vertex?
a
+q
4.
+q
Two opposite charges are separated by 5.0 cm as shown in the picture. Find the E-field (a)
10 cm directly above the point midway between the charges; (b) 10 cm directly to the right
of the point midway between the charged (c) midway between the charges.
2 C
5 cm
-2 C
5.
A thin glass rod is bent into a quarter of a circle of radius r. A charge +Q is uniformly
distributed on the rod. Find the electric field at the center of the quarter circle.
+Q
r
6.
In his famous experiment that demonstrated quantization of electric charge, Millikan
suspended small oil drops in a electric field. With a field strength of 2 x 107 N/C, what mass
drop can be suspended when the drop carries a net charge of 10 elementary charges?
7.
What is the acceleration of an electron in a uniform electric field of 1.4 x 106 N/C? How
long would it take for the electron, starting from rest, to attain one-tenth the speed of light?
How far would it travel in that time?
8.
A dipole with dipole moment 1.5 x 10-9 C m is orientated at 30° to an electric field of 4 x
106 N/C. (a) What is the magnitude of the torque on the dipole? (b) How much work is
required to turn the dipole so that it is antiparallel to the field?