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 29, Problem 29.30P
(a)
To determine
The observations are important or not.
(b)
To determine
The observations are important or not.
(c)
To determine
The comparison of the charge to mass ratio obtained by JJ Thomson.
(d)
To determine
Whether Thomson observe any deflection of beam due to gravitation.
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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 29 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 29 - An electron moves in the plane of this paper...Ch. 29 - Prob. 29.2QQCh. 29 - A wire carries current in the plane of this paper...Ch. 29 - (i) Rank the magnitudes of the torques acting on...Ch. 29 - Prob. 29.1OQCh. 29 - Rank the magnitudes of' the forces exerted on the...Ch. 29 - A particle with electric charge is fired into a...Ch. 29 - A proton moving horizontally enters a region where...Ch. 29 - Prob. 29.5OQCh. 29 - A thin copper rod 1.00 in long has a mass of 50.0...
Ch. 29 - Prob. 29.7OQCh. 29 - Classify each of die following statements as a...Ch. 29 - An electron moves horizontally across the Earths...Ch. 29 - A charged particle is traveling through a uniform...Ch. 29 - In the velocity selector shown in Figure 29.13....Ch. 29 - Prob. 29.12OQCh. 29 - A magnetic field exerts a torque on each of the...Ch. 29 - Can a constant magnetic field set into motion an...Ch. 29 - Explain why it is not possible to determine the...Ch. 29 - Is it possible to orient a current loop in a...Ch. 29 - How can the motion of a moving charged particle be...Ch. 29 - Prob. 29.5CQCh. 29 - Charged panicles from outer space, called cosmic...Ch. 29 - Two charged particles are projected in the same...Ch. 29 - At the equator, near the surface of the Earth, the...Ch. 29 - Determine the initial direction of the deflection...Ch. 29 - Find the direction of the magnetic field acting on...Ch. 29 - Consider an electron near the Earths equator. In...Ch. 29 - Prob. 29.5PCh. 29 - A proton moving at 4.00 106 m/s through a...Ch. 29 - An electron is accelerated through 2.40 103 V...Ch. 29 - A proton moves with a velocity of v = (2i 4j + k)...Ch. 29 - A proton travels with a speed of 5.02 106 m/s in...Ch. 29 - A laboratory electromagnet produces a magnetic...Ch. 29 - A proton moves perpendicular to a uniform magnetic...Ch. 29 - Review. A charged particle of mass 1.50 g is...Ch. 29 - An electron moves in a circular path perpendicular...Ch. 29 - An accelerating voltage of 2.50103 V is applied to...Ch. 29 - A proton (charge + e, mass mp), a deuteron (charge...Ch. 29 - A particle with charge q and kinetic energy K...Ch. 29 - Review. One electron collides elastically with a...Ch. 29 - Review. One electron collides elastically with a...Ch. 29 - Review. An electron moves in a circular path...Ch. 29 - Review. A 30.0-g metal hall having net charge Q =...Ch. 29 - A cosmic-ray proton in interstellar space has an...Ch. 29 - Assume the region to the right of a certain plane...Ch. 29 - A singly charged ion of mass m is accelerated from...Ch. 29 - A cyclotron designed to accelerate protons has a...Ch. 29 - Prob. 29.25PCh. 29 - Singly charged uranium-238 ions are accelerated...Ch. 29 - A cyclotron (Fig. 28.16) designed to accelerate...Ch. 29 - A particle in the cyclotron shown in Figure 28.16a...Ch. 29 - Prob. 29.29PCh. 29 - Prob. 29.30PCh. 29 - Prob. 29.31PCh. 29 - A straight wire earning a 3.00-A current is placed...Ch. 29 - A conductor carrying a current I = 15.0 A is...Ch. 29 - A wire 2.80 m in length carries a current of 5.00...Ch. 29 - A wire carries a steady current of 2.40 A. A...Ch. 29 - Why is the following situation impossible? Imagine...Ch. 29 - Review. A rod of mass 0.720 kg and radius 6.00 cm...Ch. 29 - Review. A rod of mass m and radius R rests on two...Ch. 29 - A wire having a mass per unit length of 0.500 g/cm...Ch. 29 - Consider the system pictured in Figure P28.26. A...Ch. 29 - A horizontal power line oflength 58.0 in carries a...Ch. 29 - A strong magnet is placed under a horizontal...Ch. 29 - Assume the Earths magnetic field is 52.0 T...Ch. 29 - In Figure P28.28, the cube is 40.0 cm on each...Ch. 29 - Prob. 29.45PCh. 29 - A 50.0-turn circular coil of radius 5.00 cm can be...Ch. 29 - A magnetized sewing needle has a magnetic moment...Ch. 29 - A current of 17.0 mA is maintained in a single...Ch. 29 - An eight-turn coil encloses an elliptical area...Ch. 29 - Prob. 29.50PCh. 29 - A rectangular coil consists of N = 100 closely...Ch. 29 - A rectangular loop of wire has dimensions 0.500 m...Ch. 29 - A wire is formed into a circle having a diameter...Ch. 29 - A Hall-effect probe operates with a 120-mA...Ch. 29 - Prob. 29.55PCh. 29 - Prob. 29.56APCh. 29 - Prob. 29.57APCh. 29 - Prob. 29.58APCh. 29 - A particle with positive charge q = 3.20 10-19 C...Ch. 29 - Figure 28.11 shows a charged particle traveling in...Ch. 29 - Review. The upper portion of the circuit in Figure...Ch. 29 - Within a cylindrical region of space of radius 100...Ch. 29 - Prob. 29.63APCh. 29 - (a) A proton moving with velocity v=ii experiences...Ch. 29 - Review. A 0.200-kg metal rod carrying a current of...Ch. 29 - Prob. 29.66APCh. 29 - A proton having an initial velocity of 20.0iMm/s...Ch. 29 - Prob. 29.68APCh. 29 - A nonconducting sphere has mass 80.0 g and radius...Ch. 29 - Why is the following situation impossible? Figure...Ch. 29 - Prob. 29.71APCh. 29 - A heart surgeon monitors the flow rate of blood...Ch. 29 - A uniform magnetic Held of magnitude 0.150 T is...Ch. 29 - Review. (a) Show that a magnetic dipole in a...Ch. 29 - Prob. 29.75APCh. 29 - Prob. 29.76APCh. 29 - Consider an electron orbiting a proton and...Ch. 29 - Protons having a kinetic energy of 5.00 MeV (1 eV...Ch. 29 - Review. A wire having a linear mass density of...Ch. 29 - A proton moving in the plane of the page has a...
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