Quiz
A charged particle with positive charge q1is fixed at the
point x=a, y=b.
y
d
b
q2
q1
a
c
x
What are the x and y components of the force on a particle
with positive charge q2 which is fixed at the point x = c, y = d?
The negative charge of electron has
exactly the same magnitude as the
positive charge of the proton.
Neutral atom
Positive ion
Negative ion
Charging of neutral objects
By contact:
a)
q1  0; q2  0
q
q
b)
q1  Q
q2  0
q1  q2  Q
Q
Q
2
2
How you can make a balloon stick to the wall?
Principle of Superposition
(revisited)
The presence of other charges does not change the force exerted by
point charges. One can obtain the total force by adding or
superimposing the forces exerted by each particle separately.
Suppose we have a number N of charges scattered in some region.
We want to calculate the force that all of these charges exert on some
test charge q0 .
q3
q2
q1
q7
q8
q5
q0
q4
q6


1  q0 q1rˆ1 q0 q2 rˆ2
1
 2  2  ... 
Fq0 
40  r1
r2
 40
q0 qi rˆi
.

2
ri
i 1
N


1  q0 q1rˆ1 q0 q2 rˆ2
1
 2  2  ... 
Fq0 
40  r1
r2
 40
q0 qi rˆi
.

2
ri
i 1
N
N 
We introduce the charge density or charge per unit volume

q

How do we calculate the total force acting on the test charge
q?
We chop the blob up into little chunks of volume V ; each
chunk contains charge q  V . Suppose there are N
chunks, and we label each of them with some index .
i
q
r̂i
Let r̂i be the unit vector pointing from i th chunk to the
test charge; let ri be the distance between chunk and
test charge. The total force acting on the test charge is
 N 1 q( Vi )rˆi
F 
2
4

r
i 1
0
i
This is approximation!
The approximation becomes exact if we let the number of chunks go to
infinity and the volume of each chunk go to zero – the sum then becomes
an integral:

1 qdV rˆ
F 
2
4

r
0
V
If the charge is smeared over a surface, then we integrate a surface
charge density
over the area of the surface A:


1 qdA rˆ
F 
2
4

r
0
A
If the charge is smeared over a line, then we integrate a line charge
density
over the area of the length:

Problem 6 page 10
Suppose a charge q were fixed at the origin and
an amount of charge Q were uniformly distributed
along the x-axis from x=a to x=a+L. What would
be the force on the charge at the origin?
Another example on force due to a
uniform line charge
A rod of length L has a total charge Q smeared
uniformly over it. A test charge q is a distance a
away from the rod’s midpoint. What is the force
that the rod exerts on the test charge?

dx
( x  c)
2
3
2
x

c( x  c)
2
1
2

xdx
( x 2  c)
3
2

1
( x 2  c)
1
2
Another example on force due to a
uniform line charge
A rod of length L has a total charge Q smeared
uniformly over it. A test charge q is a distance a
away from the rod’s midpoint. What is the force
that the rod exerts on the test charge?

dx
( x  c)
2
3
2
x

c( x  c)
2
1
2

xdx
( x 2  c)
3
2

1
( x 2  c)
1
2
Have a great day!
Hw: All Chapter 2 problems
and exercises
Reading: Chapter 2