University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
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Textbook Question
Chapter 13, Problem 84CP
The accompanying figure shows a metal disk of inner radius r1 and other radius r2 rotating at an
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Check out a sample textbook solutionStudents have asked these similar questions
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 13 Solutions
University Physics Volume 2
Ch. 13 - Chek sour Understanding A closely und coil has a...Ch. 13 - Check ‘sour Und.rtanding Find the dhectlon of the...Ch. 13 - Check Your UnderstAnding Verify the directions of...Ch. 13 - Check Your Understanding Shown below is a rod of...Ch. 13 - Check Your Understanding A rod of length 10cm...Ch. 13 - Check Your understanding Suppose that the coil of...Ch. 13 - Check Your Understanding What Is the magnitude of...Ch. 13 - Check your Understanding Themagneticfield shown...Ch. 13 - Check Your Understanding A long solenoid of...Ch. 13 - A stationary coil is in a magnetic field that is...
Ch. 13 - In Faraday’s experiments, what would be the...Ch. 13 - A copper ring and a wooden ring of the same...Ch. 13 - Discuss the factors determining the induced emf in...Ch. 13 - a. Does the induced emf in a circuit depend on the...Ch. 13 - How would changing the radius of loop D shown...Ch. 13 - Can there be an induced emf in a circuit at an...Ch. 13 - Does the induced emf always act to decrease the...Ch. 13 - How would you position a flat loop of wire in a...Ch. 13 - The normal to tt plane of a single-turn conducting...Ch. 13 - The circular conducting loops shown in the...Ch. 13 - The north pole of a mag’iet is moved toward a...Ch. 13 - The accompanying figure shows a conducting ring at...Ch. 13 - Show that and dm/dt have the same units.Ch. 13 - State the direction of the induced current for...Ch. 13 - A bar magnet falls under the influence of gravity...Ch. 13 - Around the geographic North Pole (or magnetic...Ch. 13 - A wire loop moves translationally (no rotation) in...Ch. 13 - Is the work required to accelerate a rod from rest...Ch. 13 - The copper sheet shown below is partially in a...Ch. 13 - A conducting sheet lies in a plane perpendicular...Ch. 13 - Electromagnetic braking can be achieved by...Ch. 13 - A coil is moved through a magnetic field as shown...Ch. 13 - A 50-turn coil has a diameter of 15 cm. The coil...Ch. 13 - Repeat your calculations of the preceding...Ch. 13 - A square loop whose sides are 6.0-cm long is made...Ch. 13 - The magnetic field through a circular loop of...Ch. 13 - The accompanying figure shows a single-turn...Ch. 13 - How would the answers to the preceding problem...Ch. 13 - A long solenoid with n= 10 turns per centimeter...Ch. 13 - A rectangular wire loop with length a and width b...Ch. 13 - The magnetic field perpendicular to a single sire...Ch. 13 - A single-turn circular loop of wire of radius 50...Ch. 13 - When a magnetic field is first turned on, t1 flux...Ch. 13 - The magnetic flux through the loop shown in the...Ch. 13 - Use Lenz’s law to determine tl direction of...Ch. 13 - An automobile with a radio antenna 1.0 m long...Ch. 13 - Prob. 38PCh. 13 - Suppose the magnetic field of the preceding...Ch. 13 - A coil of 1000 turns encloses an area of 25 cm2....Ch. 13 - In the circuit sho in the accompanying figure, the...Ch. 13 - The rod shown in the accompanying figure is moving...Ch. 13 - A 25-cm nod moves at 5.0 m/s in a plane...Ch. 13 - In the accompanying figure, the rails, connecting...Ch. 13 - The rod shown below moves to the right on...Ch. 13 - Shown below is a conducting rod that slides along...Ch. 13 - Calculate the induced electric field in a 50-tuni...Ch. 13 - The magnetic field through a circular loop of...Ch. 13 - The current I through a long solenoid with n trims...Ch. 13 - Calculate the electric field induced both inside...Ch. 13 - Prob. 51PCh. 13 - The magnetic field at all points within the...Ch. 13 - The current in a long solenoid of radius 3 cm is...Ch. 13 - The current in a long solenoid of radius 3 cm and...Ch. 13 - Design a current loop that, when rotated in a...Ch. 13 - A flat, square coil of 20 turns that has sides of...Ch. 13 - A 50-turn rectangular coil with dimensions...Ch. 13 - The square armature coil of an alternating current...Ch. 13 - A flip coil is a relatively simple device used to...Ch. 13 - The flip coil of the preceding problem has a...Ch. 13 - A 120-V, series-wound motor has a field resistance...Ch. 13 - A small series-wound dc motor is operated from a...Ch. 13 - Shown in the following figure is a long, straight...Ch. 13 - A metal bar of mass 500 g slides outward at a...Ch. 13 - A current is induced in a circular loop of radius...Ch. 13 - A metal bar of length 25 cm is placed...Ch. 13 - A coil with 50 turns and area 10cm2 is oriented...Ch. 13 - A 2-turn planer loop of flexible wire is placed...Ch. 13 - The conducting rod shown in the accompanying...Ch. 13 - A circular loop of wire of radius 10 cm is mounted...Ch. 13 - The magnetic field between the poles of a...Ch. 13 - A long solenoid of radius a with n turns per unit...Ch. 13 - A 120-V, series-wound dc motor draws 0.50 A from...Ch. 13 - The armature and field coils of a series-wound...Ch. 13 - A copper wire of Length I is fashioned into a...Ch. 13 - A 0.50-kg copper sheet drops through a uniform...Ch. 13 - A circular copper disk of radius 7.5 on rotates at...Ch. 13 - A short rod of length a moves with its velocity...Ch. 13 - A rectangular circuit containing a resistance R is...Ch. 13 - Two infinite solenoids cross the plane of the...Ch. 13 - An eight-turn coil is tightly wrapped around the...Ch. 13 - Shown below is a long rectangular loop of width w,...Ch. 13 - A square bar of mass m and resistance R is sliding...Ch. 13 - The accompanying figure shows a metal disk of...Ch. 13 - A long solenoid with 10 turns per centimeter is...Ch. 13 - The current in the long, straight wire shown in...Ch. 13 - A 500-turn coil with a 0.250m2 area is spun in...Ch. 13 - A circular loop of wire of radius 10 cm. is...Ch. 13 - A long solenoid of radius a with n turns per unit...Ch. 13 - A rectangular copper loop of mass 100 g and...Ch. 13 - A metal bar of mass m slides without friction over...Ch. 13 - A time-dependent uniform magnetic field of...
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