Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 32, Problem 32.67AP
(a)
To determine
The inductance of the flat, compact, circular coil with radius R
N
(b)
To determine
The order of magnitude of the inductance.
(c)
To determine
The order of time constant that describes that how fast current is moving of the inductance when switch is switched off.
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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]
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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)
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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.
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Suppose that A, is a covector field, and consider the object
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Chapter 32 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 32 - A coil with zero resistance has its ends labeled a...Ch. 32 - Prob. 32.2QQCh. 32 - Prob. 32.3QQCh. 32 - Prob. 32.4QQCh. 32 - (i) At an instant of time during the oscillations...Ch. 32 - Prob. 32.1OQCh. 32 - Prob. 32.2OQCh. 32 - Prob. 32.3OQCh. 32 - In Figure OQ32.4, the switch is left in position a...Ch. 32 - Prob. 32.5OQ
Ch. 32 - Prob. 32.6OQCh. 32 - Prob. 32.7OQCh. 32 - Prob. 32.1CQCh. 32 - Prob. 32.2CQCh. 32 - A switch controls the current in a circuit that...Ch. 32 - Prob. 32.4CQCh. 32 - Prob. 32.5CQCh. 32 - Prob. 32.6CQCh. 32 - The open switch in Figure CQ32.7 is thrown closed...Ch. 32 - After the switch is dosed in the LC circuit shown...Ch. 32 - Prob. 32.9CQCh. 32 - Discuss the similarities between the energy stored...Ch. 32 - Prob. 32.1PCh. 32 - Prob. 32.2PCh. 32 - Prob. 32.3PCh. 32 - Prob. 32.4PCh. 32 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 32 - Prob. 32.6PCh. 32 - Prob. 32.7PCh. 32 - Prob. 32.8PCh. 32 - Prob. 32.9PCh. 32 - Prob. 32.10PCh. 32 - Prob. 32.11PCh. 32 - A toroid has a major radius R and a minor radius r...Ch. 32 - Prob. 32.13PCh. 32 - Prob. 32.14PCh. 32 - Prob. 32.15PCh. 32 - Prob. 32.16PCh. 32 - Prob. 32.17PCh. 32 - Prob. 32.18PCh. 32 - Prob. 32.19PCh. 32 - When the switch in Figure P32.18 is closed, the...Ch. 32 - Prob. 32.21PCh. 32 - Show that i = Iiet/ is a solution of the...Ch. 32 - Prob. 32.23PCh. 32 - Consider the circuit in Figure P32.18, taking =...Ch. 32 - Prob. 32.25PCh. 32 - The switch in Figure P31.15 is open for t 0 and...Ch. 32 - Prob. 32.27PCh. 32 - Prob. 32.28PCh. 32 - Prob. 32.29PCh. 32 - Two ideal inductors, L1 and L2, have zero internal...Ch. 32 - Prob. 32.31PCh. 32 - Prob. 32.32PCh. 32 - Prob. 32.33PCh. 32 - Prob. 32.34PCh. 32 - Prob. 32.35PCh. 32 - Complete the calculation in Example 31.3 by...Ch. 32 - Prob. 32.37PCh. 32 - A flat coil of wire has an inductance of 40.0 mH...Ch. 32 - Prob. 32.39PCh. 32 - Prob. 32.40PCh. 32 - Prob. 32.41PCh. 32 - Prob. 32.42PCh. 32 - Prob. 32.43PCh. 32 - Prob. 32.44PCh. 32 - Prob. 32.45PCh. 32 - Prob. 32.46PCh. 32 - In the circuit of Figure P31.29, the battery emf...Ch. 32 - A 1.05-H inductor is connected in series with a...Ch. 32 - A 1.00-F capacitor is charged by a 40.0-V power...Ch. 32 - Calculate the inductance of an LC circuit that...Ch. 32 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 32 - Prob. 32.52PCh. 32 - Prob. 32.53PCh. 32 - Prob. 32.54PCh. 32 - An LC circuit like the one in Figure CQ32.8...Ch. 32 - Show that Equation 32.28 in the text Ls Kirchhoffs...Ch. 32 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 32 - Consider an LC circuit in which L = 500 mH and C=...Ch. 32 - Electrical oscillations are initiated in a series...Ch. 32 - Review. Consider a capacitor with vacuum between...Ch. 32 - Prob. 32.61APCh. 32 - An inductor having inductance I. and a capacitor...Ch. 32 - A capacitor in a series LC circuit has an initial...Ch. 32 - Prob. 32.64APCh. 32 - When the current in the portion of the circuit...Ch. 32 - At the moment t = 0, a 24.0-V battery is connected...Ch. 32 - Prob. 32.67APCh. 32 - Prob. 32.68APCh. 32 - Prob. 32.69APCh. 32 - At t = 0, the open switch in Figure P31.46 is...Ch. 32 - Prob. 32.71APCh. 32 - Prob. 32.72APCh. 32 - Review. A novel method of storing energy has been...Ch. 32 - Prob. 32.74APCh. 32 - Review. The use of superconductors has been...Ch. 32 - Review. A fundamental property of a type 1...Ch. 32 - Prob. 32.77APCh. 32 - In earlier times when many households received...Ch. 32 - Assume the magnitude of the magnetic field outside...Ch. 32 - Prob. 32.80CPCh. 32 - To prevent damage from arcing in an electric...Ch. 32 - One application of an RL circuit is the generation...Ch. 32 - Prob. 32.83CP
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