Physics for Scientists and Engineers, Volume 2
10th Edition
ISBN: 9781337553582
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 30, Problem 3P
Scientific work is currently under way to determine whether weak oscillating magnetic fields can affect human health. For example, one study found that drivers of trains had a higher incidence of blood cancer than other railway workers, possibly due to long exposure to mechanical devices in the train engine cab. Consider a magnetic field of magnitude 1.00 × 10−3 T, oscillating sinusoidally at 60.0 Hz. If the diameter of a red blood cell is 8.00 μm, determine the maximum emf that can be generated around the perimeter of a cell in this 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 30 Solutions
Physics for Scientists and Engineers, Volume 2
Ch. 30.1 - A circular loop of wire is held in a uniform...Ch. 30.2 - In Figure 30.8a, a given applied force of...Ch. 30.3 - Figure 30.12 Figure 30.12 shows a circular loop of...Ch. 30.5 - Prob. 30.4QQCh. 30 - A circular loop of wire of radius 12.0 cm is...Ch. 30 - An instrument based on induced emf has been used...Ch. 30 - Scientific work is currently under way to...Ch. 30 - A long solenoid has n = 400 turns per meter and...Ch. 30 - An aluminum ring of radius r1 = 5.00 cm and...Ch. 30 - An aluminum ring of radius r1 and resistance R is...
Ch. 30 - A coil formed by wrapping 50 turns of wire in the...Ch. 30 - When a wire carries an AC current with a known...Ch. 30 - A toroid having a rectangular cross section (a =...Ch. 30 - A small airplane with a wingspan of 14.0 m is...Ch. 30 - A helicopter (Fig. P30.11) has blades of length...Ch. 30 - A 2.00-m length of wire is held in an eastwest...Ch. 30 - A metal rod of mass m slides without friction...Ch. 30 - Prob. 14PCh. 30 - Prob. 15PCh. 30 - An astronaut is connected to her spacecraft by a...Ch. 30 - You are working for a company that manufactures...Ch. 30 - You are working in a laboratory that uses motional...Ch. 30 - You are working in a factory that produces long...Ch. 30 - You are working in a factory that produces long...Ch. 30 - Within the green dashed circle show in Figure...Ch. 30 - Prob. 22PCh. 30 - Prob. 23PCh. 30 - Figure P30.24 (page 820) is a graph of the induced...Ch. 30 - The rotating loop in an AC generator is a square...Ch. 30 - In Figure P30.26, a semicircular conductor of...Ch. 30 - Prob. 27PCh. 30 - Suppose you wrap wire onto the core from a roll of...Ch. 30 - A rectangular loop of area A = 0.160 m2 is placed...Ch. 30 - A rectangular loop of area A is placed in a region...Ch. 30 - A circular coil enclosing an area of 100 cm2 is...Ch. 30 - Consider the apparatus shown in Figure P30.32: a...Ch. 30 - A guitars steel string vibrates (see Fig. 30.5)....Ch. 30 - Why is the following situation impossible? A...Ch. 30 - A conducting rod of length = 35.0 cm is free to...Ch. 30 - Magnetic field values are often determined by...Ch. 30 - The plane of a square loop of wire with edge...Ch. 30 - In Figure P30.38, the rolling axle, 1.50 m long,...Ch. 30 - Figure P30.39 shows a stationary conductor whose...Ch. 30 - Prob. 40APCh. 30 - Figure P30.41 shows a compact, circular coil with...Ch. 30 - Review. In Figure P30.42, a uniform magnetic field...Ch. 30 - An N-turn square coil with side and resistance R...Ch. 30 - A conducting rod of length moves with velocity v...Ch. 30 - A long, straight wire carries a current given by I...Ch. 30 - A rectangular loop of dimensions and w moves with...Ch. 30 - A thin wire = 30.0 cm long is held parallel to...Ch. 30 - An induction furnace uses electromagnetic...Ch. 30 - Prob. 49CPCh. 30 - A betatron is a device that accelerates electrons...Ch. 30 - Review. The bar of mass m in Figure P30.51 is...
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