COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Textbook Question
Chapter 18, Problem 60PE
Integrated Concepts
A 5.00 g charged insulating ball hangs or a 30.0 cm long string in a uniform horizontal electric field as shown in Figure 18.56. Given the charge on the ball is 1,00 μC, find the strength of the field.
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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 18 Solutions
COLLEGE PHYSICS
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To...Ch. 18 - Prob. 25CQCh. 18 - Prob. 26CQCh. 18 - Given the polar character of water molecules,...Ch. 18 - Why must the test charge q in the definition of...Ch. 18 - Are the direction and magnitude of the Coulomb...Ch. 18 - Compare and contrast the Coulomb force field and...Ch. 18 - Prob. 31CQCh. 18 - A cell membrane is a thin layer enveloping a cell....Ch. 18 - Common static electricity involves charges ranging...Ch. 18 - If 1.801020electrons move through a pocket...Ch. 18 - To start a car engine, the car battery moves...Ch. 18 - A certain lightning bolt moves 40.0 C of charge....Ch. 18 - Suppose a speck of dust in an electrostatic...Ch. 18 - An amoeba has 1.001016protons and a net charge of...Ch. 18 - A 50.0 g ball of copper has a net charge of 2.00...Ch. 18 - What net charge would you place on a 100 g piece...Ch. 18 - How many coulombs of positive charge are there in...Ch. 18 - Prob. 10PECh. 18 - Prob. 11PECh. 18 - Prob. 12PECh. 18 - Prob. 13PECh. 18 - Prob. 14PECh. 18 - Prob. 15PECh. 18 - Prob. 16PECh. 18 - Prob. 17PECh. 18 - Prob. 18PECh. 18 - Prob. 19PECh. 18 - Prob. 20PECh. 18 - Prob. 21PECh. 18 - Prob. 22PECh. 18 - Prob. 23PECh. 18 - What is the repulsive force between two pith balls...Ch. 18 - (a) How strong is the attractive force between a...Ch. 18 - Two point charges exert a 5.00 N force on each...Ch. 18 - Two point charges are brought closer together,...Ch. 18 - How far apart must two point charges of 75.0 nC...Ch. 18 - If two equal charges each of 1 C each are...Ch. 18 - A test charge of +2C is placed halfway between a...Ch. 18 - Bare free charges do not remain stationary when...Ch. 18 - (a) By what factor must you change the distance...Ch. 18 - Suppose you have a total charge qtot that you can...Ch. 18 - (a) Common transparent tape becomes charged when...Ch. 18 - Find the ratio of the electrostatic to...Ch. 18 - At what distance is the electrostatic force...Ch. 18 - A certain five cent coin contains 5.00 g of...Ch. 18 - (a) Two point charges totaling 8.00 C exert a...Ch. 18 - Point charges of 5.00 C and 3.00/C are placed...Ch. 18 - (a) Two point charges q1 and q23.00 m apart, and...Ch. 18 - What is the magnitude and direction of an electric...Ch. 18 - What is the magnitude and direction of the force...Ch. 18 - Calculate the magnitude of the electric field 2.00...Ch. 18 - (a) What magnitude point charge creates a 10,000...Ch. 18 - Calculate the initial (from rest) acceleration of...Ch. 18 - (a) Find the direction and magnitude of an...Ch. 18 - (a) Sketch the electric field lines near a point...Ch. 18 - Prob. 48PECh. 18 - Prob. 49PECh. 18 - Prob. 50PECh. 18 - (a) What is the electric field 5.00 m from the...Ch. 18 - (a) What is the direction and magnitude of an...Ch. 18 - Prob. 53PECh. 18 - Earth has a net charge that produces an electric...Ch. 18 - Point charges of 25.0 C and 45.0 (2 are placed...Ch. 18 - What can you say about two charges q1and q2, if...Ch. 18 - Integrated Concepts Calculate the angular velocity...Ch. 18 - Integrated Concepts An electron has an initial...Ch. 18 - Integrated Concepts The practical limit to an...Ch. 18 - Integrated Concepts A 5.00 g charged insulating...Ch. 18 - Integrated Concepts Figure 18.57 shows an electron...Ch. 18 - Integrated Concepts The classic Millikan oil drop...Ch. 18 - Integrated Concepts (a) In Figure 18.59, four...Ch. 18 - Unreasonable Results 64. (a) Calculate the...Ch. 18 - Unreasonable results (a) Two 0.500 g raindrops in...Ch. 18 - Unreasonable results A wrecking yard inventor...Ch. 18 - Construct Your Own Problem Consider two insulating...Ch. 18 - Construct Your Own Problem Consider identical...Ch. 18 - Prob. 1TPCh. 18 - Prob. 2TPCh. 18 - Prob. 3TPCh. 18 - Prob. 4TPCh. 18 - Prob. 5TPCh. 18 - Prob. 6TPCh. 18 - Prob. 7TPCh. 18 - Prob. 8TPCh. 18 - Prob. 9TPCh. 18 - Prob. 10TPCh. 18 - Prob. 11TPCh. 18 - Prob. 12TPCh. 18 - Prob. 13TPCh. 18 - Prob. 14TPCh. 18 - Prob. 15TPCh. 18 - Prob. 16TPCh. 18 - Prob. 17TPCh. 18 - Prob. 18TPCh. 18 - Prob. 19TPCh. 18 - Prob. 20TPCh. 18 - Prob. 21TPCh. 18 - Prob. 22TPCh. 18 - Prob. 23TPCh. 18 - Prob. 24TPCh. 18 - Prob. 25TPCh. 18 - Prob. 26TPCh. 18 - Prob. 27TPCh. 18 - Prob. 28TPCh. 18 - Prob. 29TPCh. 18 - Prob. 30TPCh. 18 - Prob. 31TPCh. 18 - Prob. 32TPCh. 18 - Prob. 33TPCh. 18 - Prob. 34TPCh. 18 - Prob. 35TPCh. 18 - Prob. 36TPCh. 18 - Prob. 37TPCh. 18 - Prob. 38TPCh. 18 - Prob. 39TPCh. 18 - Prob. 40TPCh. 18 - Prob. 41TP
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