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Unformatted text preview: / 10/19/09
Mean; 51.2 Ph213 — Exam 1 Show: 22 Name: Slot #z 1. The velocity of a "blah wave" in air is 10 m/sec. A source, S, of blah waves {at left below) moves to
the left at 6 m/sec. S emits a blah wave every 0.4 sec. A detector, D, of blah waves (at right) moves to
the right at 5 m/sec. Yes, you will be Working with actual numbers in this problem. a) Determine the wavelength and frequency of the detected wave by using the “two step method” l
showed you in lecture (the method also used in my notes.) Briefly explain what you are doing in each of the two steps. Do not derive or make use of the Lancg Doggler formulas. (12%) b) if detector D reflects the blah waves back to source S, describe qualitatively what a person moving with
source 8 would experience (what they would hear or see or... whatever one does to perceive “blah waves”).
Nothing fancy needed here, just a few words. {3%) ——¢———b——I—b———
3 10 m/s D 2. A charge distribution is spherically symmetric, but not uniform. It produces an electric ﬁeld of magnitude E = Kr“,
pointing radially outward from the sphere’s center, where r is the radial distance from the center, and K is a constant.
(The function I{r4 is the electric ﬁeld throughout all space.) Find the volume density, p, of the charge distribution. (20%) 3. The figure below shows an infinitely long insulating cylindrical charge distribution of radius ’a’ and constant volume
charge density p lying along the x—axis. At the origin of the coordinate system is a spherical "air bubble" (i.e., zero charge
distribution) of radius 'b’, where b < a. a) Find an exact expression for the electric field at point P, a distance 'Y’along the yaxis. Note that point P is outside
(above) the cylinder (i.e., Y > a). (14%) b) Suppose that the p of the cylinder was not constant, but was a function of r, the radial cylindrical coordinate (i.e., the
perpendicular distance from the xaxis). Would this change your approach (ifat all) to part a? Don’t calculate anything, just explain in words. (2%) c) Is your approach to part a valid for a > r > b? What specific changes are necessary, if any? (2%) d) Is your approach to part a valid for point P' [which is located at an arbitrary x coordinate)?
What specific cha nges are necessary, if any? {2%) Reminder of cylindrical coordinates 4. A source, 5, of3 cm (wavelength) microwaves sits at the origin. It emits 3dimensional (spherical) waves that travel in all directions. Consider three rays that leave 5 and eventually arrive at point P (located at (X,0)). * Ray #1 starts out along the positive y axis, bounces off microwave reflector R1, and then heads directly to point P. * Ray #2 starts out along the negative x axis, bounces off reflector R2 at (—4 cm, 0), and then heads directly to point P. * Ray #3 heads directly along the positive x axis to get to P. Each reﬂected microwave acquires a it phase shift in bouncing off of a reflector. ignore the dependence of amplitude upon distance in this problem. A table of square roots has been provided (since you may not use a calculator). Use the values in this table, even though
they are not very accurate. 3) Take X to be 10 cm. Carefully draw a phasor diagram on the graph paper provided and use it to determine,
approximately, the amplitude of the resultant wave at point P. Do your best to get an accurate anSWEr without a
protractor or ruler. Label your phasor diagram — indicate which phasor corresponds to each ray. (17%] lo) Redo pa rt 3 in the limit X —> 00 (Le, point P remains on the x axis, but moves far to the right). (5%} c) In this particular problem, how does the phasor diagram evolve (change shape) as point P is located at increasing
values ofx along the x axis? (3%) .5.
5. A piece of plastic has been bent into a semi—circle of radius r. Its linear charge distribution is M8} = W [C/m]
ﬂ'CDS where B is measured from the horizontal axis. Setup gig solve for the field produced at point P. Include a carefully
labeled sketch. (20%) ...
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