Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 22, Problem 29P
Calculate the magnitude of the magnetic field at a point 25.0 cm from a long, thin conductor carrying a current of 2.00 A.
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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 22 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 22.2 - An electron moves in the plane of this paper...Ch. 22.3 - A charged particle is moving perpendicular to a...Ch. 22.5 - A wire carries current in the plane of this paper...Ch. 22.7 - Consider the magnetic field due to the current in...Ch. 22.8 - Prob. 22.5QQCh. 22.9 - Figure 22.30 (Quick Quiz 22.6) Four closed paths...Ch. 22.9 - Prob. 22.7QQCh. 22.10 - Consider a solenoid that is very long compared...Ch. 22 - Prob. 1OQCh. 22 - What creates a magnetic field? More than one...
Ch. 22 - A charged particle is traveling through a uniform...Ch. 22 - A proton moving horizontally enters a region where...Ch. 22 - Two long, parallel wires each carry the same...Ch. 22 - Two long, straight wires cross each other at a...Ch. 22 - Prob. 7OQCh. 22 - Prob. 8OQCh. 22 - Answer each question yes or no. (a) Is it possible...Ch. 22 - A long, straight wire carries a current I (Fig....Ch. 22 - A thin copper rod 1.00 m long has a mass of 50.0...Ch. 22 - A magnetic field exerts a torque on each of the...Ch. 22 - Two long, parallel wires carry currents of 20.0 A...Ch. 22 - Prob. 14OQCh. 22 - A long solenoid with closely spaced turns carries...Ch. 22 - Solenoid A has length L and N turns, solenoid B...Ch. 22 - Prob. 1CQCh. 22 - Prob. 2CQCh. 22 - Prob. 3CQCh. 22 - Prob. 4CQCh. 22 - Prob. 5CQCh. 22 - Prob. 6CQCh. 22 - Prob. 7CQCh. 22 - Imagine you have a compass whose needle can rotate...Ch. 22 - Prob. 9CQCh. 22 - Can a constant magnetic field set into motion an...Ch. 22 - Prob. 11CQCh. 22 - Prob. 12CQCh. 22 - Prob. 13CQCh. 22 - Prob. 14CQCh. 22 - A proton travels with a speed of 3.00 106 m/s at...Ch. 22 - Determine the initial direction of the deflection...Ch. 22 - An electron is accelerated through 2.40 103 V...Ch. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - Review. An electron moves in a circular path...Ch. 22 - A cosmic-ray proton in interstellar space has an...Ch. 22 - Prob. 11PCh. 22 - Prob. 12PCh. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Consider the mass spectrometer shown schematically...Ch. 22 - Prob. 16PCh. 22 - The picture tube in an old black-and-white...Ch. 22 - Prob. 18PCh. 22 - Prob. 19PCh. 22 - In Figure P22.20, the cube is 40.0 cm on each...Ch. 22 - Prob. 21PCh. 22 - Prob. 22PCh. 22 - A wire 2.80 m in length carries a current of 5.00...Ch. 22 - A current loop with magnetic dipole moment is...Ch. 22 - A rectangular coil consists of N = 100 closely...Ch. 22 - Prob. 26PCh. 22 - Prob. 27PCh. 22 - Prob. 28PCh. 22 - Calculate the magnitude of the magnetic field at a...Ch. 22 - An infinitely long wire carrying a current I is...Ch. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - One long wire carries current 30.0 A to the left...Ch. 22 - Prob. 34PCh. 22 - Prob. 35PCh. 22 - Prob. 36PCh. 22 - Prob. 37PCh. 22 - 3. In Niels Bohr’s 1913 model of the hydrogen...Ch. 22 - Review. In studies of the possibility of migrating...Ch. 22 - Prob. 40PCh. 22 - Prob. 41PCh. 22 - Prob. 42PCh. 22 - In Figure P22.43, the current in the long,...Ch. 22 - Prob. 44PCh. 22 - Prob. 45PCh. 22 - Prob. 46PCh. 22 - Prob. 47PCh. 22 - A packed bundle of 100 long, straight, insulated...Ch. 22 - Prob. 49PCh. 22 - Prob. 50PCh. 22 - Prob. 51PCh. 22 - Prob. 52PCh. 22 - A long, straight wire lies on a horizontal table...Ch. 22 - Prob. 54PCh. 22 - A single-turn square loop of wire, 2.00 cm on each...Ch. 22 - Prob. 56PCh. 22 - A long solenoid that has 1 000 turns uniformly...Ch. 22 - A solenoid 10.0 cm in diameter and 75.0 cm long is...Ch. 22 - Prob. 59PCh. 22 - In Niels Bohr’s 1913 model of the hydrogen atom,...Ch. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 63PCh. 22 - Prob. 64PCh. 22 - Prob. 65PCh. 22 - The Hall effect finds important application in the...Ch. 22 - Prob. 67PCh. 22 - Prob. 68PCh. 22 - Prob. 69PCh. 22 - Prob. 70PCh. 22 - Assume the region to the right of a certain plane...Ch. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Review. Rail guns have been suggested for...Ch. 22 - Prob. 77PCh. 22 - Prob. 78PCh. 22 - Prob. 79PCh. 22 - Prob. 80PCh. 22 - Prob. 81P
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