Physics I
Class 21
Electric Fields II
21-1
Class #20
Take-Away Concepts (Review)
1.
Electric field from point charge sources:
(Total field is the superposition of point source fields.)

E  
1 qi
r̂
2 i
4   0 ri
2.
Force on a charge in an electric field:
3.
4.
Electric field points away from + source charges.
Electric field points toward – source charges.


F  qE
21-2
The Electric Field of a Point
Charge (as a Source)
The electric field is a vector field, meaning at each point in
space the electric field has a magnitude and a direction. We
show that by drawing arrows at representative points in the
correct directions with lengths proportional to the magnitudes.
Away from positive
Toward negative
+
-
Just because we don’t draw an electric field vector at
a point doesn’t mean there is no electric field there.
21-3
How to Solve Problems Asking
“Where is Net Electric Field = 0?”
+X
Region I
Region II
+ charge
Region III
- charge
Many things to consider:
 The number of regions (N+1) is one more than number of charges (N).
 The total electric field is the sum of the individual fields from each charge.
(Principle of Superposition)
 In each region, the direction of electric field from each charge is constant in that region.
(Away from +, toward –.)
 The magnitude of electric field depends on the value of charge and inverse distance squared
to the charge.
 In any region, if you get close enough to one of the charges at the end points, the inverse
distance squared dependence will make the field from that charge much larger than the
fields from all of the other charges.
 If you get far enough away from all the charges in Region I or Region N+1, the inverse
distance term is about the same for all points, so the relative sizes of the electric fields from
each charge will be determined by the sizes of the charges.
 In a region where the total electric field is zero at some location, it will point in one direction
at one end of the region and the other direction somewhere else in the region – the middle or
the opposite end.
21-4
How to Solve Problems Asking
“Where is Net Electric Field = 0?”
+X
Region I
Region II
Region III
+7 C
-4 C
Region I:
E field from +7C direction is to the left.
E field from –4C direction is to the right.
Every point is closer to +7C than to –4C, so net field is always to the left.
No points where E = 0.
Region II:
E field from +7C direction is to the right.
E field from –4C direction is to the right.
Net field is always to the right.
No points where E = 0.
Region III:
E field from +7C direction is to the right.
E field from –4C direction is to the left.
Close to –4C, net E field is to the left.
Far from –4C, net E field is to the right because 7 > 4 and far enough away the inverse
distance squared will be about the same for both.
There is one point where E = 0.
21-5
How to Solve Problems Asking
“Where is Net Electric Field = 0?”
+X
Region I
Region II
+7 C
d
Region III
-4 C
x-d
x
1 7
1
4

0
4   0 x 2 4   0 ( x  d) 2
7
4

x 2 ( x  d) 2
7
2

x x d
7 ( x  d)  2 x
x
7
d  4.097 d
72
21-6
Class #21
Take-Away Concepts
To find points where E = 0, consider the following:
1. Consider N+1 regions for N charges on a line.
2. Superposition Principle: Add E from each charge.
3. E points away from + charge, toward – charge.
4. E depends on charge value and inverse distance squared.
5. Very close to a charge, E from that charge dominates.
6. Far away right or left, all distances are about the same.
7. Look for reversal of total E direction in a region.
21-7
Activity #21
Electric Fields II
(Pencil and Paper Activity)
Objective of the Activity:
1.
2.
3.
Think about the relationship of force and field.
Finding points where E = 0.
Introduction to electric dipoles.
21-8