Lab 4: Electric Field of a Uniformly Charged Rod
Lab 4:
Electric Field of a Uniformly Charged Rod
OBJECTIVES
In this lab you will
Diagram the plane for a complex VPython program
Create a program to display the E field form a charged rod at any point
Practice calculating the E field due to charged objects
From class and the text, you have learned that there is a relatively simple formula for finding the
Electric field on the central, perpendicular axis of a uniformly charge rod:
±²
³
´µ¶
·
¸
¹
º»º
¼
½ ¾¿ À
Á Â
¼
Ã Ä
³
´µ¶
·
À ¹ ¿
Á
º
where
r
is the distance from the midpoint of the rod to the observation location,
Q
is the total
charge of the rod, and
L
is the length of the rod.
If the rod is significantly longer than the
distance
r,
then the Electric Field is approximately equal to the rightmost expression above. If
Q
is positive, the field is radially away from the rod, and if
Q
is negative, the Efield is directed
radially inward.
To calculate the electric field at other locations, you must perform a difficult integral.
You will
make VPython do something approaching an integral by modeling a charged rod as a line of
point charges.
If you then make the number of point charges very large, VPython will do a
summation that is almost as accurate as an integral.
You will write a VPython program to allow
you to easily calculate the electric field, due to a charged rod, at any point in space.
1) Warm Up Problem
Problem 1)
Redraw the figure below in your work space and show an approximate
location where the electric field will be perpendicular to the rod (note the non uniform
charge distribution).
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2) Program Design
The rod you will be using has a length 2 m, and a total charge of 3 x 10
8
C. You will divide the
rod into N number of pieces (6 to begin), which you will approximate by point charges. Then
you will apply the superposition principle to get the net field at the observation location.
In your program, you will write a loop to “step” through the rod piece by piece, starting at the
left end and moving to the right.
You will find the E field from each small piece and then sum
those fields to get the net field.
The following tasks and questions will help you create algebraic
expressions for important quantities to use in the program.
Consider a rod of length 2 m, oriented along the xaxis, with the center of the rod at the origin.
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 Spring '07
 k
 Charge, Electric charge, rod

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