Physics 208 Dr Tatiana Erukhimova Lecture 4 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 ID: 539596
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Slide1
Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 4Slide2
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:Slide3
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?Slide4
The electric field
y
x
has the same direction as Slide5
Michael Faraday
1791-1867
“
The best experimentalist in the history of science
”Slide6
Electric field lines
These are fictitious lines we sketch which point in the direction of the electric field. 1) The direction of at any point is tangent to the line of force at that point. 2) The density of lines of force in any region is proportional to the magnitude of in that region
Lines never cross.Slide7Slide8Slide9
How to calculate ?
1) Put a
“
test charge
”
at some point and do not allow it to move any other charges
2) Calculate the electric force on and divide by to obtain
The force that
N
charges exert on a test charge :
Slide10
We also calculated the force that a blob of charged material with charge density exerts on a test charge:
We wrote the similar formulas if the charge is smeared out over a surface with surface density , or over a line with line density .
In all of these cases, the force ends up proportional to the test charge . We might factor it out. This is the electric field! Slide11
(
N
point charges)
(Charge continuum)
Given an electric field, we can calculate force exerted on some point charge :Slide12
Example 1: Electric field of a point charge is directly radially away from or toward the charge.
Example 2:
Electric field of a dipoleSlide13
Example 3: Electric field at the center of a charged ring
Think first!
(before you start doing calculations)Slide14
Example 4:
Find the electric field at the center of a semi-circle of radius R, if a charge Q is uniformly spread over the semi-circle.
OSlide15
Have a great day!
Hw: All Chapter 2 problems and exercises
Reading: Chapter 2