College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Textbook Question
Chapter 24, Problem 22PE
(a) What is the wavelength of 100−MHz radio waves used in an MRI unit? (b) If the frequencies are swept over a (
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 24 Solutions
College Physics For Ap® Courses
Ch. 24 - The direction of the electric field shown in each...Ch. 24 - Is the direction of the magnetic field shown in...Ch. 24 - Why is the direction of the current shown in each...Ch. 24 - In which situation shown in Figure 24.24 will the...Ch. 24 - In which situation shown in Figure 24.25 will the...Ch. 24 - Should the straight wire antenna of a radio he...Ch. 24 - Under what conditions might wires in a DC circuit...Ch. 24 - Give an example of interference of electromagnetic...Ch. 24 - Figure 24.26 shows the interference pattern of two...Ch. 24 - Can an antenna be any length? Explain your answer.
Ch. 24 - If you live in a region that has a particular TV...Ch. 24 - Explain why people who have the lens of their eye...Ch. 24 - How do ?uorescent soap residues make clothing look...Ch. 24 - Give an example of resonance in the reception of...Ch. 24 - Illustrate that the size of details of an object...Ch. 24 - Why don't buildings block radio waves as...Ch. 24 - Make a list of some everyday objects and decide...Ch. 24 - Your friend says mat more patterns and colors can...Ch. 24 - The rate at which information can be transmitted...Ch. 24 - Give an example of energy carried by an...Ch. 24 - In an MRI scan, a higher magnetic field requires...Ch. 24 - Laser vision correction often uses an excimer...Ch. 24 - Verify that the correct value for the speed of...Ch. 24 - Show that, when SI units for 0 and 0 are entered,...Ch. 24 - What is the maximum electric field strength in an...Ch. 24 - The maximum magnetic field strength of an...Ch. 24 - Verify the units obtained for magnetic field...Ch. 24 - (a) Two microwave frequencies are authorized for...Ch. 24 - (a) Calculate the range of wavelength for AM radio...Ch. 24 - A radio station utilizes frequencies between...Ch. 24 - Find the frequency range of visible light, given...Ch. 24 - Combing your hair leads to excess electrons on the...Ch. 24 - Electromagnetic radiation having a 15.0m...Ch. 24 - Approximately what is the smallest detail...Ch. 24 - A radar used to detect the presence of aircraft...Ch. 24 - Some radar systems detect the size and shape of...Ch. 24 - Determine the amount of time it takes for X-rays...Ch. 24 - If you wish to detect details of the size of atoms...Ch. 24 - If the Sun suddenly turned off, we would not know...Ch. 24 - Distances in space are often quoted in units of...Ch. 24 - A certain 50.0-Hz AC power line radiates an...Ch. 24 - During normal bee?ng, the heat creates a maximum...Ch. 24 - (a) The ideal size (most efficient) for a...Ch. 24 - (a) What is the wavelength of 100MHz radio waves...Ch. 24 - (a) What is the frequency at the 193-nm...Ch. 24 - TV-reception antennas for VHF are constructed with...Ch. 24 - Conversations with astronauts on lunar walks had...Ch. 24 - Lunar astronauts placed a reflector on the Moon's...Ch. 24 - Radar is used to determine distances to various...Ch. 24 - Integrated Concepts (a) Calculate the ratio of the...Ch. 24 - Integrated Concepts (a) Calculate the rate in...Ch. 24 - What is the intensity of an electromagnetic wave...Ch. 24 - Find the intensity of an electromagnetic wave...Ch. 24 - Assume the helium-neon lasers commonly used in...Ch. 24 - An AM radio transmitter broadcasts 50.0 kW of...Ch. 24 - Suppose the maximum safe intensity of microwaves...Ch. 24 - A 2.50-m-diameter university communications...Ch. 24 - Lasers can be constructed that produce an...Ch. 24 - Show that for a continuous sinusoidal...Ch. 24 - Suppose a source of electromagnetic waves radiates...Ch. 24 - Integrated Concepts An LC circuit with a 5.00pF...Ch. 24 - Integrated Concepts What capacitance is needed in...Ch. 24 - Integrated Concepts Police radar determines the...Ch. 24 - Integrated Concepts Assume the mostly infrared...Ch. 24 - Integrated Concepts On its highest power se1ting,...Ch. 24 - Integrated Concepts Electromagnetic radiation from...Ch. 24 - Integrated Concepts A 200-turn flat coil of wire...Ch. 24 - Integrated Concepts If electric and magnetic field...Ch. 24 - Unreasonable Results A researcher measures the...Ch. 24 - Unreasonable Results The peak magnetic field...Ch. 24 - Unreasonable Results An LC circuit containing a...Ch. 24 - Unreasonable Results An LC circuit containing a...Ch. 24 - Create Your Own Problem Consider electromagnetic...Ch. 24 - Create Your Own Problem Consider the most recent...
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