Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 23, Problem 4P
To determine
The vector force exerted on
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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]
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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
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(b)…
Chapter 23 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 23.1 - Three objects are brought close to each other, two...Ch. 23.2 - Three objects are brought close to one another,...Ch. 23.3 - Object A has a charge of +2 C, and object B has a...Ch. 23.4 - A test charge of +3 C is at a point P where an...Ch. 23.6 - Rank the magnitudes of the electric field at...Ch. 23 - Prob. 1OQCh. 23 - Prob. 2OQCh. 23 - Prob. 3OQCh. 23 - Prob. 4OQCh. 23 - Prob. 5OQ
Ch. 23 - Prob. 6OQCh. 23 - Prob. 7OQCh. 23 - Prob. 8OQCh. 23 - Prob. 9OQCh. 23 - Prob. 10OQCh. 23 - Prob. 11OQCh. 23 - Prob. 12OQCh. 23 - Prob. 13OQCh. 23 - Prob. 14OQCh. 23 - Prob. 15OQCh. 23 - Prob. 1CQCh. 23 - A charged comb often attracts small bits of dry...Ch. 23 - Prob. 3CQCh. 23 - Prob. 4CQCh. 23 - Prob. 5CQCh. 23 - Prob. 6CQCh. 23 - Prob. 7CQCh. 23 - Prob. 8CQCh. 23 - Prob. 9CQCh. 23 - Prob. 10CQCh. 23 - Prob. 11CQCh. 23 - Find to three significant digits the charge and...Ch. 23 - Prob. 2PCh. 23 - Prob. 3PCh. 23 - Prob. 4PCh. 23 - In a thundercloud, there may be electric charges...Ch. 23 - (a) Find the magnitude of the electric force...Ch. 23 - Prob. 7PCh. 23 - Nobel laureate Richard Feynman (19181088) once...Ch. 23 - A 7.50-nC point charge is located 1.80 m from a...Ch. 23 - Prob. 10PCh. 23 - Prob. 11PCh. 23 - Prob. 12PCh. 23 - Prob. 13PCh. 23 - Prob. 14PCh. 23 - Prob. 15PCh. 23 - Prob. 16PCh. 23 - Review. In the Bohr theory of the hydrogen atom,...Ch. 23 - Prob. 18PCh. 23 - Prob. 19PCh. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Why is the following situation impossible? Two...Ch. 23 - Prob. 23PCh. 23 - Prob. 24PCh. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - Prob. 27PCh. 23 - Prob. 28PCh. 23 - Prob. 29PCh. 23 - Prob. 30PCh. 23 - Prob. 31PCh. 23 - Two charged particles are located on the x axis....Ch. 23 - Prob. 33PCh. 23 - Two 2.00-C point charges are located on the x...Ch. 23 - Prob. 35PCh. 23 - Consider the electric dipole shown in Figure...Ch. 23 - A rod 14.0 cm long is uniformly charged and has a...Ch. 23 - Prob. 38PCh. 23 - A uniformly charged ring of radius 10.0 cm has a...Ch. 23 - The electric field along the axis of a uniformly...Ch. 23 - Prob. 41PCh. 23 - Prob. 42PCh. 23 - A continuous line of charge lies along the x axis,...Ch. 23 - Prob. 44PCh. 23 - Prob. 45PCh. 23 - Prob. 46PCh. 23 - A negatively charged rod of finite length carries...Ch. 23 - Prob. 48PCh. 23 - Prob. 49PCh. 23 - Prob. 50PCh. 23 - A proton accelerates from rest in a uniform...Ch. 23 - Prob. 52PCh. 23 - Prob. 53PCh. 23 - Protons are projected with an initial speed vi =...Ch. 23 - Prob. 55PCh. 23 - Prob. 56PCh. 23 - A proton moves at 4.50 105 m/s in the horizontal...Ch. 23 - Prob. 58APCh. 23 - Consider an infinite number of identical...Ch. 23 - A particle with charge 3.00 nC is at the origin,...Ch. 23 - Prob. 61APCh. 23 - Prob. 62APCh. 23 - Prob. 63APCh. 23 - Prob. 64APCh. 23 - Prob. 65APCh. 23 - Prob. 66APCh. 23 - Prob. 67APCh. 23 - Prob. 68APCh. 23 - Prob. 69APCh. 23 - Two point charges qA = 12.0 C and qB = 45.0 C and...Ch. 23 - Prob. 71APCh. 23 - Prob. 72APCh. 23 - Two small spheres hang in equilibrium at the...Ch. 23 - Prob. 74APCh. 23 - Prob. 75APCh. 23 - Prob. 76APCh. 23 - Prob. 77APCh. 23 - Prob. 78APCh. 23 - Prob. 79APCh. 23 - Prob. 80APCh. 23 - Prob. 81APCh. 23 - Prob. 82APCh. 23 - Prob. 83APCh. 23 - Identical thin rods of length 2a carry equal...Ch. 23 - Prob. 85CPCh. 23 - Prob. 86CPCh. 23 - Prob. 87CPCh. 23 - Prob. 88CPCh. 23 - Prob. 89CPCh. 23 - Prob. 90CPCh. 23 - Two particles, each with charge 52.0 nC, are...
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