Physics 112 Computing Lab:
Finite Element Analysis
The goals of this exercise are as follows:


Become familiar with the method of finite element analysis.
Gain experience and familiarity with the methods for calculating E by hand.
Consider a rod with uniform charge +Q and length 2a, oriented as in the figure below.
E
y
φ
P
a
+Q
x
ROD
–a
a
We want to find the electric field (magnitude and direction) at point P due to the rod. We will do so three
different ways:
I. Crude Approximation
A. Approximate the rod as a single point charge of +Q at the origin, and calculate the magnitude and
⃗ |=
direction of this point charge at point P. Leave your magnitude in terms of a number times kQ/a2 (|𝑬
𝑘𝑄
𝑎2
where you need to fill in the blank), but you should get a numerical answer for φ. Although this
is a simple calculation, it is rather inaccurate.
B. Approximate the rod as two point charges, each of charge +Q/2. One point charge is at x = -a/2,
and the other is at x = +a/2. Again, leave your magnitude in terms of a number times kQ/a2, and you
should get a numerical answer for φ. This calculation is not as simple as A, but it is a little more
accurate.
II. Finite Element Analysis
Ohmann/Jalkio/Thomas – UST Physics
Finite element analysis involves breaking up a continuous object into discrete chunks, which we
approximate as points. In the limit that these chunks get very small, the approximation becomes better
and the calculation approaches the exact continuous result. This technique is especially useful since it
can be programmed into a computer, which can then be used to grind out the calculation very accurately.
In this case, we’ll be using Microsoft Excel to help us calculate the field as a number times kQ/a2.
Fire up your laptop and download the Excel spreadsheet “finite element analysis.xls” from our course
web site. This is *very* easy to use! At the very top of the spreadsheet, there is a yellow shaded area
that says “Input number of segments here →→→→→” followed by a box with a number in it. The
number in this box is the number of segments you break the rod into. All you need to do is type in this
box the number of segments you wish to break the rod up into, and the spreadsheet automatically spits
out the magnitude of E at point P (as a number times kQ/a2) and the angle φ in degrees.
A. As in IA, approximate the rod as one point charge at the origin by typing a “1” in the appropriate
box. Record the magnitude of E and φ. Are these the same as what you got in IA?
B. Break the rod into two segments, and record the magnitude of E and φ. Are these the same as what
you got in part IB?
C. Repeat with smaller (more) segments (e.g., 4, 10, 20, etc.) and record the results. You may split
the rod into as many as 1000 segments.
D. Plot the magnitude of the electric field vs. number of segments. Also plot the angle φ vs. number
of segments. Do both the magnitude and angle converge?
III. Exact Continuous Calculation
A. Now calculate the electric field at P exactly using the appropriate integrals (one for Ex, one for Ey,
and combining them correctly). Actually DO the integrals (you may use your favorite mathematics
software to do so)! Your answer should again be in the form of a number times kQ/a2.
B. Compare the exact results to your results from I and II above. Do the values for the magnitude and
angle that finite element analysis yields converge to the exact answer? If so, what is the fewest
number of segments that the rod must be broken up into in order to get within 1% of the correct
answer?
You need not turn in a formal lab report for this exercise. However, you must turn in all of your calculations,
values for E and φ (from your calculations and the spreadsheet), and the graphs of E vs. # of segments and
φ vs. # of segments. All calculations, graphs, and answers to questions must be clear enough that your
fellow students can follow them. This will count as a lab, not a group problem.
This exercise will be graded on the following criteria (total of 5 points):
5 points – Everything is correct and easy to follow.
4 points – Everything is neat and tidy, but only half of it is correct. OR most is correct but is very difficult
to follow.
3 points – You do everything but it is all incorrect.
Ohmann/Jalkio/Thomas – UST Physics
0 points – You turn in nothing.
Ohmann/Jalkio/Thomas – UST Physics