Problem
A set of 10 charges are sparsely distributed in a plane spanned by the two unit vectors
^x and ^y. Assuming that charges are immobile, You need to nd a point where the
total electric eld due to all charges vanishes (equals zero). You will need to write a
computer program that will help you nd the point needed. A MATLAB code will
be the easier way of getting the job done.
The charges and their x-y coordinates are given in the following table:
Index 1 2 3 4 5 6 7 8 9 10
Charge (in pC) 10 5.967 10.167 6.409 3.164 10.168 3.248 6.409 1.788 1.788
X - Position 1.6 1.246 2.822 3.176 1.683 4.378 1.061 4.024 2.93 3.845
Y - Position 1.86 3.506 1.082 4.284 4.084 2.638 4.048 3.437 4.84 4.435
Hints
- Try to write the vector equation of the Electric eld due to one charge placed
in a general position Xi; Yi, at a general point X; Y , and then sum over all given
charges,i = 1; 2; ::; 10.
- In MATLAB, if you want to check if X == 0, you would rather check for X <<
0:0001 because equality conditions do not return correct answers due to imperfect
representation of
oating numbers in nite-length memory word size..
Bonus - Those who hand over the assignment during the rst 5 days after the
publication of the assignment (up till Thursday 22th Dec: 2011 at 23:59) will receive
massive amount of bonus marks that may be added to their midterm mark.
- After the bonus deadline (mentioned previously), an extra hint will be given and
another deadline will be set for another bonus mark that will be of less value than
the previous.
- A known algorithm for minimization is the Genetic Algorithm (GA). Students who
2
are able to solve the problem using GA in MATLAB will receive a massive bonus
that will be added to their midterm mark. Note that GA in MATLAB is
implemented using the two functions ga and gaoptimset. You can look for those two
functions in MATLAB for a thorough explanation of how they are used.
A set of 10 charges are sparsely distributed in a plane spanned by the two unit vectors
^x and ^y. Assuming that charges are immobile, You need to nd a point where the
total electric eld due to all charges vanishes (equals zero). You will need to write a
computer program that will help you nd the point needed. A MATLAB code will
be the easier way of getting the job done.
The charges and their x-y coordinates are given in the following table:
Index 1 2 3 4 5 6 7 8 9 10
Charge (in pC) 10 5.967 10.167 6.409 3.164 10.168 3.248 6.409 1.788 1.788
X - Position 1.6 1.246 2.822 3.176 1.683 4.378 1.061 4.024 2.93 3.845
Y - Position 1.86 3.506 1.082 4.284 4.084 2.638 4.048 3.437 4.84 4.435
Hints
- Try to write the vector equation of the Electric eld due to one charge placed
in a general position Xi; Yi, at a general point X; Y , and then sum over all given
charges,i = 1; 2; ::; 10.
- In MATLAB, if you want to check if X == 0, you would rather check for X <<
0:0001 because equality conditions do not return correct answers due to imperfect
representation of
oating numbers in nite-length memory word size..
Bonus - Those who hand over the assignment during the rst 5 days after the
publication of the assignment (up till Thursday 22th Dec: 2011 at 23:59) will receive
massive amount of bonus marks that may be added to their midterm mark.
- After the bonus deadline (mentioned previously), an extra hint will be given and
another deadline will be set for another bonus mark that will be of less value than
the previous.
- A known algorithm for minimization is the Genetic Algorithm (GA). Students who
2
are able to solve the problem using GA in MATLAB will receive a massive bonus
that will be added to their midterm mark. Note that GA in MATLAB is
implemented using the two functions ga and gaoptimset. You can look for those two
functions in MATLAB for a thorough explanation of how they are used.
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