Download Meaning of Electric Field

The Electric Field
(Chapter 22.1-5)
A.
Meaning of Electric Field?
Consider Coulomb’s Law describing force between charges q1 and q2 separated by distance r:
F 
k q1 q 2
r2
Why does q2 ‘feel’ force?
 Can think of it as q1 setting up a ‘force field’ that q2 has entered
 The field is there irrespective of the presence of q2
 The field exerts a force per charge on a charge q2 that enters it.
kq
F
 21 r̂ , where we are assuming q1 is a point charge, and r̂ is unit vector
q2
r
pointing away from q1.
Thus
E
Electric field is a vector field, i.e., a region of space that has vectors associated
with each location. The direction of the vector is the direction of force a
positive test charge would experience at that location. The magnitude of the
vector is the force/per charge a test charge would experience at that location.
(Discuss similarities to the gravitational field)
B.
Visualizing Electric Fields
Represented visually different ways
 Electric field lines (see figures 22-2b to 22-5 on pages 582 and 583)
 Electric field vectors (see figure 22-6 on page 584)
Electric Field vectors
C.
Electric Fields of Simple Charge Configurations
Electric field due to a point charge, q1, is given as in the above: E 
F kq1
 2 rˆ
q2
r
If there is more than one source, we must do vector addition to get net field due to all sources,
treating each source as a point source.
Example: Like Problem 12, page 598
Calculate the direction and magnitude of the electric field at point P due to the three point
charges.
+q
+q
X
P
a
+2q
a
P
X
a
+q
+2q
a
+q
The E-field contributions by the +q charges cancel each other out. The magnitude of the
contribution to the E-field by the +2q charge is:
E 
k q1
r
2

k ( 2q )
1

a2  a2 

2

2

2kq 4kq
 2
1 2
a
a
2
The direction is given by the remaining arrow pointing to the upper right.
Visualizing Three Special Cases:
 Two positive charges
 Two negative charges
 One positive and one negative charge
D.
Electric Field due to Electric Dipole
Special case of E at distance z from electric dipole
Assumes z >> d
E 
kqd kp
 3 where p is electric dipole moment
z3
z
(see pages 585-587 for development)
z
+
d
-
E.
Electric Fields and Conductors
Charge a conductor. How does the charge distribute itself?
 Sphere
 Spherical shell
 Arbitrary solid shape
What is the electric field like inside a charged conductor?
How do electric field lines ‘meet’ a conductor?