College Physics
1st Edition
ISBN: 9781938168048
Author: Paul Peter Urone, OpenStax, Roger Hinrichs
Publisher: OpenStax
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Textbook Question
Chapter 22, Problem 23CQ
Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.
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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
College Physics
Ch. 22 - Volcanic and other such activity at the...Ch. 22 - Explain why the magnetic field would not be unique...Ch. 22 - List the ways in which magnetic field lines and...Ch. 22 - Noting that the magnetic field lines of a bar...Ch. 22 - Is the Earth's magnetic field parallel to the...Ch. 22 - If a charged particle moves in a straight line...Ch. 22 - How can the motion of a charged particle be used...Ch. 22 - High-velocity charged particles can damage...Ch. 22 - If a cosmic ray proton approaches the Earth from...Ch. 22 - What are the signs of the charges on the particles...
Ch. 22 - Which of the particles in Figure 22.47 has the...Ch. 22 - Which of the particles in Figure 22.47 has the...Ch. 22 - While operating, a high-precision TV monitor is...Ch. 22 - Discuss how the Hall effect could be used to...Ch. 22 - Draw a sketch of the situation in Figure 22.30...Ch. 22 - Verify than the direction of the line force in an...Ch. 22 - Why would a magnetohydrodynamic drive work better...Ch. 22 - Which is more likely to interfere with compass...Ch. 22 - Draw a diagram and use RHR-l to show that the...Ch. 22 - Make a drawing and use RHR—2 to find the direction...Ch. 22 - Is the force attractive or repulsive between the...Ch. 22 - It you have three parallel wires in the same...Ch. 22 - Suppose two long straight wires run perpendicular...Ch. 22 - Use the right hand rules to show that the force...Ch. 22 - If one of the loops in Figure 22.49 is titled...Ch. 22 - Electric field lines can be shielded by me Faraday...Ch. 22 - Measurements at the weak and ?uctuating magnetic...Ch. 22 - Discuss the possibility that a Hall voltage would...Ch. 22 - A patient in an MRI unit turns his head quickly to...Ch. 22 - You are told that in a certain region there is...Ch. 22 - An example of magnetohydrodynamics (MHD) comes...Ch. 22 - Draw gravitational field lines between 2 masses,...Ch. 22 - What is the direction of the magnetic force on a...Ch. 22 - Repeal Exercise 22.1 for a negative charge.Ch. 22 - What is the direction of the velocity of a...Ch. 22 - Repeal Exercise 22.3 for a positive charge.Ch. 22 - What is the direction of the magnetic field that...Ch. 22 - Repeal Exercise 22.5 for a negative charge.Ch. 22 - What is the maximum force on an aluminum rod with...Ch. 22 - (a) Aircraft sometimes acquire small static...Ch. 22 - (a) A cosmic ray proton moving toward the Earth at...Ch. 22 - An electron moving at 4.00103m/s in a 1.25T...Ch. 22 - (a) A physicist performing a sensitive measurement...Ch. 22 - A cosmic ray electron moves at 7.50106m/s...Ch. 22 - A proton moves at 7.50107m/s perpendicular to a...Ch. 22 - (a) Viewers of Star Trek hear of an antimatter...Ch. 22 - (a) An oxygen16 ion with a mass at 2.661026kg...Ch. 22 - What radius circular path does an electron travel...Ch. 22 - A velocity selector in a mass spectrometer uses a...Ch. 22 - An electron in a TV CRT moves with a speed at...Ch. 22 - (a) At what speed will a proton move in a circular...Ch. 22 - A mass spectrometer is being used to separate...Ch. 22 - (a) Triply charged uranium-235 and uranium-238...Ch. 22 - A large water main is 2.50 m in diameter and the...Ch. 22 - What Hall voltage is produced by a 0.200T field...Ch. 22 - (a) What is the speed of a supersonic aircraft...Ch. 22 - A nonmechanical water meter could utilize the Hall...Ch. 22 - Calculate the Hall voltage induced on a patient’s...Ch. 22 - A Hall probe calibrated to read 1.00V when placed...Ch. 22 - Using information in Example 20.6, what would the...Ch. 22 - Show that the Hall voltage across wires made of...Ch. 22 - A patient with a pacemaker is mistakenly being...Ch. 22 - What is the direction of the magnetic force on the...Ch. 22 - What is the direction of a current that...Ch. 22 - What is the direction of the magnetic field that...Ch. 22 - (a) What is the force per meter on a lightning...Ch. 22 - (a) A DC power line for a light-rail system...Ch. 22 - What force is exerted on the water in an MHD drive...Ch. 22 - A wire carrying a 30.0-A current passes between...Ch. 22 - (a) A 0.750-m-long section of cable carrying...Ch. 22 - (a) What is the angle between a wire carrying an...Ch. 22 - The force on the rectangular loop of wire in the...Ch. 22 - (a) By how many percent is the torque of a motor...Ch. 22 - (a) What is me maximum torque on a 150Turn square...Ch. 22 - Find the current through a loop needed to create a...Ch. 22 - Calculate the magnetic field strength needed on a...Ch. 22 - Since the equation for torque on a...Ch. 22 - (a) At what angle (is the torque on a current loop...Ch. 22 - A proton has a magnetic field due to its spin on...Ch. 22 - (a) A 200Turn circular loop of radius 50.0 cm is...Ch. 22 - Repeat Exercise 22.41, but with the loop lying...Ch. 22 - (a) The hot and neutral wires supplying DC power...Ch. 22 - The force per meter between the two wires of a...Ch. 22 - A 2.50m segment of wire supplying current to the...Ch. 22 - The wire carrying 400 A to The motor of a commuter...Ch. 22 - An AC appliance cord has its hot and neutral wires...Ch. 22 - Figure 22.57 shows a long straight wire near a...Ch. 22 - Find the direction and magnitude of the force that...Ch. 22 - Find the direction and magnitude of the force that...Ch. 22 - Indicate whether the magnetic field created in...Ch. 22 - What are the directions of the fields in the...Ch. 22 - What are the directions of the currents in the...Ch. 22 - To see why an MRI utilizes iron to increase the...Ch. 22 - Inside a motor, 30.0 A passes through a 250-turn...Ch. 22 - Nonnuclear submarines use batteries for power when...Ch. 22 - How strong is the magnetic field inside a solenoid...Ch. 22 - What current is needed in the solenoid described...Ch. 22 - How far from the starter cable of a car, carrying...Ch. 22 - Measurements affect the system being measured,...Ch. 22 - Figure 22.62 shows a long straight wire just...Ch. 22 - Find the magnitude and direction of the magnetic...Ch. 22 - Find the magnitude and direction of the magnetic...Ch. 22 - What current is needed in the top wire in Figure...Ch. 22 - Calculate the size of the magnetic field 20 m...Ch. 22 - Integrated Concepts A pendulum is set up so that...Ch. 22 - Integrated Concepts (a) What voltage will...Ch. 22 - Integrated Concepts Find the radius of curvature...Ch. 22 - Integrated Concepts To construct a nonmechanical...Ch. 22 - Integrated Concepts (a) Using the values given for...Ch. 22 - Integrated Concepts (a) Calculate the maximum...Ch. 22 - Integrated Concepts A current balance used to...Ch. 22 - Integrated Concepts (a) Show that the period of...Ch. 22 - Integrated Concepts A cyclotron accelerates...Ch. 22 - Integrated Concepts (a) A 0.140-kg baseball,...Ch. 22 - Integrated Concepts (a) What is the direction of...Ch. 22 - Integrated Concepts One long straight wire is to...Ch. 22 - Unreasonable Results (a) Find the charge on a...Ch. 22 - Unreasonable Results A charged particle having...Ch. 22 - Unreasonable Results An inventor wants to generate...Ch. 22 - Unreasonable Results Frustrated by the small Hall...Ch. 22 - Unreasonable Results A surveyor 100 m from a long...Ch. 22 - Construct Your Own Problem Consider a mass...Ch. 22 - Construct Your Own Problem Consider using the...
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What is Torque? | Physics | Extraclass.com; Author: Extraclass Official;https://www.youtube.com/watch?v=zXxrAJld9mo;License: Standard YouTube License, CC-BY