Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 20, Problem 3P
Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 120 V. Calculate the speed of an electron that is accelerated through the same electric potential difference.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
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[2 marks]
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[3 marks]
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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)
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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
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Chapter 20 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 20.1 - In Figure 20. 1, two points and are located...Ch. 20.2 - The labeled points in Figure 20.4 are on a series...Ch. 20.3 - A spherical balloon contains a positively charged...Ch. 20.3 - In Active Figure 20.8a, take q1 to be a negative...Ch. 20.4 - In a certain region of space, the electric...Ch. 20.7 - A capacitor stores charge Q at a potential...Ch. 20.8 - Prob. 20.7QQCh. 20.9 - Prob. 20.8QQCh. 20.10 - If you have ever tried to hang a picture or a...Ch. 20 - A parallel-plate capacitor is charged and then is...
Ch. 20 - Prob. 2OQCh. 20 - A proton is released from rest at the origin in a...Ch. 20 - By what factor is the capacitance of a metal...Ch. 20 - Prob. 5OQCh. 20 - Rank the potential energies of the four systems of...Ch. 20 - Prob. 7OQCh. 20 - In a certain region of space, a uniform electric...Ch. 20 - Prob. 9OQCh. 20 - Prob. 10OQCh. 20 - Prob. 11OQCh. 20 - A parallel-plate capacitor is connected to a...Ch. 20 - Rank the electric potential energies of the...Ch. 20 - Four particles are positioned on the rim of a...Ch. 20 - Prob. 15OQCh. 20 - A filament running along the x axis from the...Ch. 20 - An electronics technician wishes to construct a...Ch. 20 - Prob. 18OQCh. 20 - Prob. 19OQCh. 20 - A parallel-plate capacitor filled with air carries...Ch. 20 - Prob. 21OQCh. 20 - Prob. 1CQCh. 20 - Prob. 2CQCh. 20 - Prob. 3CQCh. 20 - Prob. 4CQCh. 20 - Prob. 5CQCh. 20 - Prob. 6CQCh. 20 - Prob. 7CQCh. 20 - Prob. 8CQCh. 20 - Why is it dangerous to touch the terminals of a...Ch. 20 - Prob. 10CQCh. 20 - Prob. 11CQCh. 20 - Prob. 12CQCh. 20 - A uniform electric field of magnitude 325 V/m is...Ch. 20 - Prob. 2PCh. 20 - Calculate the speed of a proton that is...Ch. 20 - Prob. 4PCh. 20 - An electron moving parallel to the x axis has an...Ch. 20 - (a) Find the potential at a distance of 1.00 cm...Ch. 20 - Prob. 8PCh. 20 - Given two particles with 2.00-C charges as shown...Ch. 20 - Three particles with equal positive charges q are...Ch. 20 - The three charged particles in Figure P20.11 are...Ch. 20 - Prob. 12PCh. 20 - Prob. 13PCh. 20 - Review. A light, unstressed spring has length d....Ch. 20 - Review. Two insulating spheres have radii 0.300 cm...Ch. 20 - Review. Two insulating spheres have radii r1 and...Ch. 20 - Two particles each with charge +2.00 C are located...Ch. 20 - Prob. 18PCh. 20 - Two particles, with charges of 20.0 nC and 20.0...Ch. 20 - At a certain distance from a charged particle, the...Ch. 20 - A particle with charge +q is at the origin. A...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 24PCh. 20 - Prob. 25PCh. 20 - A rod of length L (Fig. P20.26) lies along the x...Ch. 20 - For the arrangement described in Problem 26,...Ch. 20 - A wire having a uniform linear charge density is...Ch. 20 - A uniformly charged insulating rod of length 14.0...Ch. 20 - How many electrons should be removed from an...Ch. 20 - Prob. 31PCh. 20 - Prob. 32PCh. 20 - (a) How much charge is on each plate of a 4.00-F...Ch. 20 - Two conductors having net charges of +10.0 C and...Ch. 20 - Prob. 35PCh. 20 - A spherical capacitor consists of a spherical...Ch. 20 - Prob. 37PCh. 20 - A variable air capacitor used in a radio tuning...Ch. 20 - Prob. 39PCh. 20 - Prob. 40PCh. 20 - (a) Regarding the Earth and a cloud layer 800 m...Ch. 20 - Prob. 42PCh. 20 - Prob. 43PCh. 20 - (a) Find the equivalent capacitance between points...Ch. 20 - Four capacitors are connected as shown in Figure...Ch. 20 - Prob. 46PCh. 20 - According to its design specification, the timer...Ch. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Three capacitors are connected to a battery as...Ch. 20 - Find the equivalent capacitance between points a...Ch. 20 - Consider the circuit shown in Figure P20.52, where...Ch. 20 - Prob. 53PCh. 20 - A parallel-plate capacitor has a charge Q and...Ch. 20 - Prob. 55PCh. 20 - Prob. 56PCh. 20 - Prob. 57PCh. 20 - Prob. 58PCh. 20 - Prob. 59PCh. 20 - Prob. 60PCh. 20 - A uniform electric field E = 3 000 V/m exists...Ch. 20 - Prob. 62PCh. 20 - Prob. 63PCh. 20 - Prob. 64PCh. 20 - Prob. 65PCh. 20 - A parallel-plate capacitor in air has a plate...Ch. 20 - Lightning can be studied with a Van de Graaff...Ch. 20 - Prob. 68PCh. 20 - Prob. 69PCh. 20 - Prob. 70PCh. 20 - Prob. 71PCh. 20 - Prob. 72PCh. 20 - Prob. 73PCh. 20 - Prob. 74PCh. 20 - Prob. 75PCh. 20 - Prob. 76PCh. 20 - Prob. 77PCh. 20 - Prob. 78PCh. 20 - Prob. 79PCh. 20 - Prob. 80PCh. 20 - Prob. 81PCh. 20 - Prob. 82PCh. 20 - A 10.0-F capacitor is charged to 15.0 V. It is...Ch. 20 - Two large, parallel metal plates, each of area A,...Ch. 20 - A capacitor is constructed from two square,...Ch. 20 - Two square plates of sides are placed parallel to...Ch. 20 - Determine the equivalent capacitance of the...
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