Download Electric Fields

Electric Charge, Force and
Field
Properties of Charge
• Unlike charges attract, like charges repel
• Force between charges varies as an inverse
square (same as gravity)
1
F 2
r
– Charge is conserved
– Charge is quantized
qe  -1.602  10 -19 C
q p  1.602 10-19 C
– p+ is 1800× heavier than e-
Benjamin Franklin
Electrical
Properties
• Conductor
– Allows easy current
– Metals
• Insulator
– Prevents current flow
– Plastics, glass, & air
• Semiconductor
– Intermediate behavior
– Carbon, silicon, & germanium
Coulomb’s Law
q2
q1
r̂
F12
F21
r

q1q2
F12  k 2 rˆ
r
k
1
40
 8.9875 109 N  m 2 / C 2
0 - Permittivity of free space
 0  8.8542 10 -12 C 2 / N  m 2
Superposition
• The net force from multiple
charges is additive.
 


F1  F21  F31  F41  
• Ex. A charge of +0.02 C is
located at the origin and a
charge of -0.05 C is located at
(10 m, 0 m). What is the force
exerted on a +0.03 C charge
located at (5 m, 5 m)?
Electric Field
• The force per unit charge experience by a

charge.
 F
E
Units (N/C)
q0
• For a point charge the electric field is
kqq0
rˆ

2
kq
r
E
 2 rˆ
q0
r
Drawing Electric
Fields
• Lines begin on positive charges
and end on negative charges.
• # of lines leaving a charge is
proportional to the magnitude of
the charge.
• Therefore, the strength of the
electric field is proportional to the
density of the electric field lines.
• No two field lines can cross.
Field Lines
• How would you draw the field lines for the
following sets of charges?
Point Charge
Dipole
Like Charges
Continuous Charge
• Use superposition to add all the

dq
infinitesimal charges, dq.
E  k 2 rˆ
r
• If charge is uniformly distributed, then
Line Charge
Q
dq  dl , where  
l
Surface Charge
Q
dq  dxdy, where  
A
Volume Charge
Q
dq  dxdydz, where  
V
Electric Field on a
Wire
• Ex. A wire has a length of 2 m and a charge
of +20 mC. What is the electric field at a
point 4 cm away from the center of the
wire? (Assume the charge is uniformly
distributed.)
Charge in a Field
• Charge will accelerate in the direction of the
electric field lines. 
 qE
a
m
• Ex. What is the acceleration of an electron
in a 25 N/C electric field?
e-
Torque on a Dipole
• Remember


  
  r  F F  qE

 
• then   qr  E
q+
qF

p  2aq rˆ
F
2a
E
   r̂ is a unit vector going from the
  p  E negative to the positive charge