College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Textbook Question
Chapter 16, Problem 47P
A 1.00-μF capacitor is charged by being connected across a 10.0-V battery. It is then disconnected from the battery and connected across an uncharged 2.00-μF capacitor. Determine the resulting charge on each capacitor.
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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 16 Solutions
College Physics
Ch. 16.1 - If an electron is released from rest in a uniform...Ch. 16.1 - If a negatively charged particle is placed at rest...Ch. 16.1 - Figure 16.3 is a graph of an electric potential as...Ch. 16.1 - If a negatively charged particle is placed at...Ch. 16.2 - Consider a collection of charges in a given region...Ch. 16.2 - A spherical balloon contains a positively charged...Ch. 16.3 - An electron initially at rest accelerates through...Ch. 16.6 - A capacitor is designed so that one plate is large...Ch. 16.7 - A parallel-plate capacitor is disconnected from a...Ch. 16.8 - A fully charged parallel-plate capacitor remains...
Ch. 16.8 - Consider a parallel-plate capacitor with a...Ch. 16 - A proton is released from rest in a uniform...Ch. 16 - An electron is released from rest in a uniform...Ch. 16 - Figure CQ16.3 shows equipotential contours in the...Ch. 16 - Rank the potential energies of the four systems of...Ch. 16 - A parallel-plate capacitor with capacitance C0...Ch. 16 - An air-filled parallel-plate capacitor with...Ch. 16 - Choose the words that make each statement correct,...Ch. 16 - Why is it important to avoid sharp edges or points...Ch. 16 - Explain why, under static conditions, all points...Ch. 16 - If you are given three different capacitors C1,...Ch. 16 - (a) Why is it dangerous to touch the terminals of...Ch. 16 - The plates of a capacitor are connected to a...Ch. 16 - Rank the electric potentials at the four points...Ch. 16 - If you were asked to design a capacitor in which...Ch. 16 - Is it always possible to reduce a combination of...Ch. 16 - Explain why a dielectric increases the maximum...Ch. 16 - A uniform electric field of magnitude 375 N/C...Ch. 16 - A proton is released from rest in a uniform...Ch. 16 - A potential difference of 90.0 mV exists between...Ch. 16 - Cathode ray tubes (CRTs) used in old-style...Ch. 16 - A constant electric field accelerates a proton...Ch. 16 - A point charge q = +40.0 C moves from A to B...Ch. 16 - Oppositely charged parallel plates are separated...Ch. 16 - (a) Find the potential difference VB required to...Ch. 16 - An ionized oxygen molecule (O+2) at point A has...Ch. 16 - On planet Tehar, the free-fall acceleration is the...Ch. 16 - An electron is at the origin, (a) Calculate the...Ch. 16 - The two charges in Figure P16.12 are separated by...Ch. 16 - (a) Find the electric potential, taking zero at...Ch. 16 - Three charges are situated at corners of a...Ch. 16 - Two point charges Q1 = +5.00 nC and Q2 = 3.00 nC...Ch. 16 - Three identical point charges each of charge q are...Ch. 16 - The three charges in Figure P16.17 are at the...Ch. 16 - A positive point charge q = +2.50 nC is located at...Ch. 16 - A proton is located at the origin, and a second...Ch. 16 - A proton and an alpha particle (charge = 2e, mass...Ch. 16 - A tiny sphere of mass 8.00 g and charge 2.80 nC is...Ch. 16 - The metal sphere of a small Van de Graaff...Ch. 16 - In Rutherfords famous scattering experiments that...Ch. 16 - Four point charges each haring charge Q are...Ch. 16 - Calculate the speed of (a) an electron and (b) a...Ch. 16 - An electric field does 1.50 103 eV of work on a...Ch. 16 - An alpha particle, which has charge 3.20 1019 C,...Ch. 16 - In the classical model of a hydrogen atom, an...Ch. 16 - Consider the Earth and a cloud layer 8.0 102 m...Ch. 16 - (a) When a 9.00-V battery is connected to the...Ch. 16 - An air-filled parallel-plate capacitor has plates...Ch. 16 - Air breaks down and conducts charge as a spark if...Ch. 16 - An air-filled capacitor consists of two parallel...Ch. 16 - A 1-megabit computer memory chip contains many...Ch. 16 - a parallel-plate capacitor with area 0.200 m2 and...Ch. 16 - A small object with a mass of 350. g carries a...Ch. 16 - Given a 2.50-F capacitor, a 6.25-F capacitor, and...Ch. 16 - Two capacitors, C1 = 5.00 F and C2 = 12.0 F, are...Ch. 16 - Find (a) the equivalent capacitance of the...Ch. 16 - Two capacitors give an equivalent capacitance of...Ch. 16 - For the system of capacitors shown in Figure...Ch. 16 - Consider the combination of capacitors in Figure...Ch. 16 - Find the charge on each of the capacitors in...Ch. 16 - Three capacitors are connected to a battery as...Ch. 16 - A 25.0-F capacitor and a 40.0-F capacitor are...Ch. 16 - (a) Find the equivalent capacitance between points...Ch. 16 - A 1.00-F capacitor is charged by being connected...Ch. 16 - Four capacitors are connected as shown in Figure...Ch. 16 - A 12.0 V battery is connected to a 4.50 F...Ch. 16 - Two capacitors, C1 = 18.0 F and C2 = 36.0 F, are...Ch. 16 - A parallel-plate capacitor has capacitance 3.00 F....Ch. 16 - Each plate of a 5.00 F capacitor stores 60.0 C of...Ch. 16 - The voltage across an air-filled parallel-plate...Ch. 16 - (a) How much charge can be placed on a capacitor...Ch. 16 - Determine (a) the capacitance and (b) the maximum...Ch. 16 - A parallel-plate capacitor has plates of area A =...Ch. 16 - A model of a red blood cell portrays the cell as a...Ch. 16 - When a potential difference of 150. V is applied...Ch. 16 - Three parallel-plate capacitors are constructed,...Ch. 16 - For the system of four capacitors shown in Figure...Ch. 16 - A parallel-plate capacitor with a plate separation...Ch. 16 - Two capacitors give an equivalent capacitance of...Ch. 16 - A parallel-plate capacitor is constructed using a...Ch. 16 - Two charges of 1.0 C and 2.0 C are 0.50 m apart at...Ch. 16 - Find the equivalent capacitance of the group of...Ch. 16 - A spherical capacitor consists of a spherical...Ch. 16 - The immediate cause of many deaths is ventricular...Ch. 16 - When a certain air-filled parallel-plate capacitor...Ch. 16 - Capacitors C1 = 6.0 F and C2 = 2.0 F are charged...Ch. 16 - Two positive charges each of charge q are fixed on...Ch. 16 - Metal sphere A of radius 12.0 cm carries 6.00 C of...Ch. 16 - An electron is fired at a speed v0 = 5.6 106 m/s...
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