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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Textbook Question
Chapter 29, Problem 29.32P
A straight wire earning a 3.00-A current is placed in a uniform magnetic field of magnitude 0.280 T directed perpendicular to the wire. (a) Find the magnitude of the magnetic force on a section of the wire having a length of 14.0 cm. (b) Explain why you can’t determine the direction of the magnetic force from the information given in the problem.
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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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