Physics 208 Dr Tatiana Erukhimova Lecture 3 A charged particle with positive charge q 1 is fixed at the point x a y b y x q 1 q 2 a c d b What are the ID: 405287
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Slide1
Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 3Slide2
A charged particle with positive charge
q
1
is fixed at the point x=a,
y
=b.
y
x
q
1
q
2
a
c
d
b
What are the
x
and
y
components of the force on a particle with positive charge
q
2
which is fixed at the point
x = c, y = d?
QuizSlide3Slide4Slide5
The negative charge of electron has exactly the same magnitude as the positive charge of the proton.
Neutral atom
Positive ion
Negative ionSlide6
Charging of neutral objects
By contact:
a)
b)Slide7
How you can make a balloon stick to the wall?
Slide8
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 .Slide9
We introduce the charge density or charge per unit volume
How do we calculate the total force acting on the test charge ? Slide10
We chop the blob up into little chunks of volume ; each chunk contains charge . Suppose there are
N
chunks, and we label each of them with some index .
Let be the unit vector pointing from th chunk to the test charge; let be the distance between chunk and test charge. The total force acting on the test charge is
This is approximation!Slide11
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:
If the charge is smeared over a
surface
, then we integrate a
surface
charge density over the area of the surface
A
:
If the charge is smeared over a
line
, then we integrate a
line
charge density over the area of the length:Slide12
Problem 6 page 10
Suppose a charge 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? Slide13
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?Slide14
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?Slide15
Have a great day!
Hw: All Chapter 2 problems and exercises
Reading: Chapter 2