Find, to 2 significant digits, the field due to two point charges, each with charge q=0.001 C=1 mC, separated by 0.001 m at test points on the line connecting the two charges; one test point is 1m from the midpoint between the charges, and a second test point is 10 m from the midpoint between the charges. Use Coulombs law for each of the point sources and combine the fields due to each source to find the net field at the test point. What is the ratio of the field at 10 m compared to the field at 1m, and how does this depend on the ratio of the distances?
Find, to 2 significant digits, the field due to two point charges, each with charge q=0.001 C=1 mC, separated by 0.001 m at test points on the line connecting the two charges; one test point is 1m from the midpoint between the charges, and a second test point is 10 m from the midpoint between the charges. Use Coulombs law for each of the point sources and combine the fields due to each source to find the net field at the test point. What is the ratio of the field at 10 m compared to the field at 1m, and how does this depend on the ratio of the distances?
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Answer all parts please
Transcribed Image Text:(c) Comparing approximation to exact numbers and comparing monopole to dipole field:
Using Coulomb's law calculate the field of a single 0.003 C source (equal to the net charge of
the system of part (a)) at a test point a distance of 1m from the source and compare to your
calculation at the same distance in part (a). Make a similar comparison for the field at a distance
of 1m from the dipole of part (b) and the field created at that distance by a point object that
has the net charge of the dipole system. (Note, by definition, a dipole as NO net charge, so you
are comparing to zero!) What is the percent error between the approximation and the exact
answer in each case?
Finally, compare the fields of the monopole (the 0.002 charge) to the dipole field, first at 1m,
and then at 10 m.
(d) Other monopoles, dipoles, and NEITHER monopole nor dipole (actually a quadrupole, but we
won't get into that):
Calculate the exact, to 2 significant figures, field for the following 3 distributions, 10 m from the
center. I identified some appropriate approximation. Explain why that approximation should
be good, and compare your exact result to it:
Two charges of 0.002 C and one of -0.001 C, distributed on a line with 0.001 m between them
(should look just like a net charge 0.003 C monopole.)
Three charges of 0.002 C, 0.002 C and -0.004 C distributed on a line with 0.001 m between them
in the order given (should look just like a dipole, with qd = (0.004 C)(0.0015m)... why?)
%3|
Three charges of 0.002, -0.004, and 0.002 C distributed on a line with 0.001 m between them in
the order given (should have a field much smaller than that of a dipole.)
(e) An induced dipole is a dipole (separated, opposite charges) whose dipole moment is caused by
the presence of some other source charge. Often, the induced dipole moment is proportional to
the electric field (due to the other sources) at the location of the dipole. For example, when a
charged piece of tape is near your finger, the charges in the neutral atoms in your finger move
in response to the tape's field at the location of the finger, and each atom in the finger becomes
a dipole. The closer the tape is to the finger, the stronger the tape's field, and the larger the
dipole moments of the atoms in the finger. Show that the force between the tape (charge Q) and
the atoms in the fingers is proportional to Q2/r³, where r is the distance between the finger and
the tape. (Notice this force decreases with distance much more quickly than the force between
two point charges!)
Transcribed Image Text:In this problem we explore the underlying reasons for using the long distance (point source far
compared to size of source) approximations for monopoles (net charge) and dipoles (no net charge
with asymmetric positive and negative charges,) and which approximation is relevant under which
circumstance.
(a) MONOPOLE, object with net charge not zero:
Find, to 2 significant digits, the field due to two point charges, each with charge q=0.001 C=1
mC, separated by 0.001 m at test points on the line connecting the two charges; one test point is
1m from the midpoint between the charges, and a second test point is 10 m from the midpoint
between the charges. Use Coulombs law for each of the point sources and combine the fields
due to each source to find the net field at the test point. What is the ratio of the field at 10 m
compared to the field at 1m, and how does this depend on the ratio of the distances?
(b) DIPOLE: object with net charge zero, asymmetric distribution of positive and negative:
Using the dipole approximation for the field of a dipole at large distances, find the field due to
a dipole made from +1 C charges separated by 10-3 m on axis (the test point is on the line
connecting the dipole charges,) at distances of 1m and 10 m from the center of the dipole. What
is the ratio of the field at 10 compared to the field at 1m, and how does this depend on the ratio
of the distances?
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