College Physics 11E Global Edition
11th Edition
ISBN: 9781337620338
Author: SERWAY/VUILLE
Publisher: CENGAGE Learning Custom Publishing
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Chapter 20.3, Problem 20.4QQ
A horizontal metal bar oriented east-west drops straight down in a location where Earth's magnetic field is due north. As a result, an emf develops between the ends. Which end is positively charged? (a) the east end (b) the west end (c) neither end carries a charge
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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 20 Solutions
College Physics 11E Global Edition
Ch. 20.2 - Prob. 20.1QQCh. 20.2 - A bar magnet is falling toward the center of a...Ch. 20.2 - Two circular loops are side by side and lie in the...Ch. 20.3 - A horizontal metal bar oriented east-west drops...Ch. 20.3 - You intend to move a rectangular loop of wire into...Ch. 20.6 - Prob. 20.6QQCh. 20 - A bar magnet is held stationary while a circular...Ch. 20 - Does dropping a magnet down a copper tube produce...Ch. 20 - Figure CQ20.3 shows three views of a circular loop...Ch. 20 - A loop of wire is placed in a uniform magnetic...
Ch. 20 - As the conducting bar in Figure CQ20.5 moves to...Ch. 20 - How is electrical energy produced in dams? (That...Ch. 20 - Figure CQ20.7 shows a slidewire generator with...Ch. 20 - As the bar in Figure CQ20.5 moves perpendicular to...Ch. 20 - Eddy current are induced currents set up in a...Ch. 20 - The switch S in Figure 20.27 is closed at t = 0...Ch. 20 - A piece of aluminum is dropped vertically downward...Ch. 20 - When the switch in Figure CQ20.12a is closed, a...Ch. 20 - Prob. 13CQCh. 20 - A magneto is used to cause the spark in a spark...Ch. 20 - A uniform magnetic field of magnitude 0.50 T is...Ch. 20 - Find the flux of Earths magnetic field of...Ch. 20 - Prob. 3PCh. 20 - A long, straight wire carrying a current of 2.00 A...Ch. 20 - Prob. 5PCh. 20 - A magnetic field of magnitude 0.300 T is oriented...Ch. 20 - A cube of edge length = 2.5 cm is positioned as...Ch. 20 - Transcranial magnetic stimulation (TMS) is a...Ch. 20 - Three loops of wire move near a long straight wire...Ch. 20 - The flexible loop in Figure P20.10 has a radius of...Ch. 20 - Inductive charging is used to wirelessly charge...Ch. 20 - Medical devices implanted inside the body are...Ch. 20 - A technician wearing a circular metal band on his...Ch. 20 - In Figure P20.14, what is the direction of the...Ch. 20 - Prob. 15PCh. 20 - Find the direction of the current in the resistor...Ch. 20 - A circular loop of wire lies below a long wire...Ch. 20 - A square, single-turn wire loop = 1.00 cm on a...Ch. 20 - Prob. 19PCh. 20 - A circular coil enclosing an area of 100 cm2 is...Ch. 20 - To monitor the breathing of a hospital patient, a...Ch. 20 - An N-turn circular wire coil of radius r lies in...Ch. 20 - A truck is carrying a steel beam of length 15.0 m...Ch. 20 - Prob. 24PCh. 20 - Prob. 25PCh. 20 - In one of NASAs space tether experiments, a...Ch. 20 - Prob. 27PCh. 20 - An astronaut is connected to her spacecraft by a...Ch. 20 - Prob. 29PCh. 20 - Prob. 30PCh. 20 - Prob. 31PCh. 20 - Prob. 32PCh. 20 - Considerable scientific work is currently under...Ch. 20 - A flat coil enclosing an area of 0.10 m2 is...Ch. 20 - A generator connected to the wheel or hub of a...Ch. 20 - A motor has coils with a resistance of 30.0 and...Ch. 20 - A coil of 10.0 turns is in the shape of an eclipse...Ch. 20 - Prob. 38PCh. 20 - Prob. 39PCh. 20 - Prob. 40PCh. 20 - Prob. 41PCh. 20 - An emf of 24.0 mV is induced in a 500-turn coil...Ch. 20 - Prob. 43PCh. 20 - Prob. 44PCh. 20 - Prob. 45PCh. 20 - Prob. 46PCh. 20 - Prob. 47PCh. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Prob. 50PCh. 20 - Prob. 51PCh. 20 - Prob. 52PCh. 20 - Additional Problems Two circular loop of wire...Ch. 20 - Prob. 54APCh. 20 - Prob. 55APCh. 20 - Prob. 56APCh. 20 - An 820-turn wire coil of resistance 24.0 is...Ch. 20 - A spacecraft is in 4 circular orbit of radius...Ch. 20 - Prob. 59APCh. 20 - Prob. 60APCh. 20 - Prob. 61APCh. 20 - Prob. 62APCh. 20 - The magnetic field shown in Figure P20.63 has a...Ch. 20 - Prob. 64APCh. 20 - In Figure P20.65 the rolling axle of length 1.50 m...Ch. 20 - An N-turn square coil with side and resistance R...Ch. 20 - A conducting rectangular loop of mass M,...
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