ACP COLLEGE PHYS 1101/1102 BUNDLE
11th Edition
ISBN: 9781337685467
Author: SERWAY
Publisher: CENGAGE L
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Chapter 19, Problem 2CQ
To determine
How would a compass point at Earths north magnetic pole.
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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 19 Solutions
ACP COLLEGE PHYS 1101/1102 BUNDLE
Ch. 19.3 - A charged particle moves in a straight line...Ch. 19.3 - The north-pole end of a bar magnet is held near a...Ch. 19.5 - As a charged particle moves freely in a circular...Ch. 19.6 - A square and a circular loop with the same area...Ch. 19.8 - Which of the following actions would double the...Ch. 19.8 - Prob. 19.6QQCh. 19 - Prob. 1CQCh. 19 - Prob. 2CQCh. 19 - How can the motion of a charged particle be used...Ch. 19 - Prob. 4CQ
Ch. 19 - The following statements are related to the force...Ch. 19 - Will a nail be attracted to either pole of a...Ch. 19 - Figure CQ19.7 shows a coaxial cable carrying...Ch. 19 - A magnet attracts a piece of iron. The iron can...Ch. 19 - Figure CQ19.9 shows four positive charges, A, B,...Ch. 19 - Is the magnetic field created by a current loop...Ch. 19 - Suppose you move along a wire at the same speed as...Ch. 19 - Why do charged particles from outer space, called...Ch. 19 - A hanging Slinky toy is attached to a powerful...Ch. 19 - How can a current loop he used to determine the...Ch. 19 - Prob. 15CQCh. 19 - Figure CQ19.16 shows four permanent magnets, each...Ch. 19 - Two charged particles are projected in the same...Ch. 19 - Prob. 18CQCh. 19 - A magnetic field exerts a torque on each of the...Ch. 19 - Consider an electron near the Earths equator. In...Ch. 19 - (a) Find the direction of the force on a proton (a...Ch. 19 - Find the direction of the magnetic field acting on...Ch. 19 - Prob. 4PCh. 19 - A laboratory electromagnet produces a magnetic...Ch. 19 - Prob. 6PCh. 19 - Electrons and protons travel from the Sun to the...Ch. 19 - An oxygen ion (O+) moves in the xy-plane with a...Ch. 19 - A proton moving at 4.00 106 m/s through a...Ch. 19 - Sodium ions (Na+) move at 0.851 m/s through a...Ch. 19 - At the equator, near the surface of Earth, the...Ch. 19 - A proton travels with a speed of 5.02 106 m/s at...Ch. 19 - An electron moves in a circular path perpendicular...Ch. 19 - Figure P19.14a is a diagram of a device called a...Ch. 19 - Prob. 15PCh. 19 - A mass spectrometer is used to examine the...Ch. 19 - Jupiters magnetic field occupies a volume of space...Ch. 19 - Electrons in Earths upper atmosphere have typical...Ch. 19 - Prob. 19PCh. 19 - A proton (charge +e, mass mp), a deuteron (charge...Ch. 19 - A particle passes through a mass spectrometer as...Ch. 19 - In Figure P19.2, assume in each case the velocity...Ch. 19 - A current I = 15 A is directed along the positive...Ch. 19 - A straight wire carrying a 3.0-A current is placed...Ch. 19 - In Figure P19.3, assume in each case the velocity...Ch. 19 - A wire having a mass per unit length of 0.500 g/cm...Ch. 19 - A wire carries a current of 10.0 A in a direction...Ch. 19 - At a certain location, Earth has a magnetic field...Ch. 19 - A wire with a mass of 1.00 g/cm is placed on a...Ch. 19 - Mass m = 1.00 kg is suspended vertically at rest...Ch. 19 - Consider the system pictured in Figure P19.31. A...Ch. 19 - A metal rod of mass m carrying a current I glides...Ch. 19 - In Figure P19.33, the cube is 40.0 cm on each...Ch. 19 - A horizontal power line of length 58 m carries a...Ch. 19 - A wire is formed into a circle having a diameter...Ch. 19 - A current of 17.0 mA is maintained in a single...Ch. 19 - An eight-turn coil encloses an elliptical area...Ch. 19 - A current-carrying rectangular wire loop with...Ch. 19 - A 6.00-turn circular coil of wire is centered on...Ch. 19 - The orientation of small satellites is often...Ch. 19 - Along piece of wire with a mass of 0.100 kg and a...Ch. 19 - A rectangular loop has dimensions 0.500 m by 0.300...Ch. 19 - A lightning bolt may carry a current of 1.00 104...Ch. 19 - A long, straight wire going through the origin is...Ch. 19 - Neurons in our bodies carry weak currents that...Ch. 19 - In 1962 measurements of the magnetic field of a...Ch. 19 - A cardiac pacemaker can be affected by a static...Ch. 19 - The two wires shown in Figure P19.48 are separated...Ch. 19 - Prob. 49PCh. 19 - Two long, parallel wires carry currents of I1 =...Ch. 19 - Two long, parallel wires carry currents of I1 =...Ch. 19 - Prob. 52PCh. 19 - The magnetic field 40.0 cm away from a long,...Ch. 19 - Prob. 54PCh. 19 - Prob. 55PCh. 19 - Prob. 56PCh. 19 - A wire with a weight per unit length of 0.080 N/m...Ch. 19 - In Figure P19.58 the current in the long, straight...Ch. 19 - A long solenoid that has 1.00 103 turns uniformly...Ch. 19 - Prob. 60PCh. 19 - It is desired to construct a solenoid that will...Ch. 19 - Certain experiments must be performed in the...Ch. 19 - Ail electron is moving at a speed of 1.0 104 in/s...Ch. 19 - Figure P19.64 is a setup that can be used to...Ch. 19 - Two coplanar and concentric circular loops of wire...Ch. 19 - An electron moves in a circular path perpendicular...Ch. 19 - Prob. 67APCh. 19 - A 0.200-kg metal rod carrying a current of 10.0 A...Ch. 19 - Using an electromagnetic flowmeter (Fig. P19.69),...Ch. 19 - A uniform horizontal wire with a linear mass...Ch. 19 - Prob. 71APCh. 19 - Two long, parallel wires, each with a mass per...Ch. 19 - Protons having a kinetic energy of 5.00 MeV are...Ch. 19 - A straight wire of mass 10.0 g and length 5.0 cm...Ch. 19 - A 1.00-kg ball having net charge Q = 5.00 C is...Ch. 19 - Two long, parallel conductors separated by 10.0 cm...
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