College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Chapter 19, Problem 31PE
A research Van de Graaff generator has a 2.00-rn- diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (C) An oxygen atom with three missing electrons is released near the Van de Graatf generator. What is its energy in MeV at this distance?
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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
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[3 marks]
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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)
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f)
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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,
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[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]
Chapter 19 Solutions
College Physics
Ch. 19 - Voltage is the common word for potential...Ch. 19 - It the voltage between two points is zero, can a...Ch. 19 - What is the relationship between voltage and...Ch. 19 - Voltages are always measured between two points....Ch. 19 - How are units of volts and electron volts related?...Ch. 19 - Discuss how potential difference and electric...Ch. 19 - What is the strength of the electric field in a...Ch. 19 - Will a negative charge, initially at rest, move...Ch. 19 - In what region of space is the potential due to a...Ch. 19 - Can the potential of a non-uniformly charged...
Ch. 19 - What is an equipotential line? What is an...Ch. 19 - Explain in your own words why equipotential lines...Ch. 19 - Can different equipotential lines cross? Explain.Ch. 19 - Does the capacitance of a device depend on the...Ch. 19 - Use the characteristics of the of the Coulomb...Ch. 19 - Give the reason why a dielectric material...Ch. 19 - How does the polar character of water molecules...Ch. 19 - Sparks will occur between the plates of an air...Ch. 19 - Water has a large dielectric constant, but it is...Ch. 19 - Membranes ii living cells, including those in...Ch. 19 - If you wish to store a large amount of energy m a...Ch. 19 - How does the energy contained in a charged...Ch. 19 - What happens to the energy stored in a capacitor...Ch. 19 - Find the ratio of speeds of an electron and a...Ch. 19 - An evacuated tube uses an accelerating voltage of...Ch. 19 - A bare helium nucleus has two positive charges and...Ch. 19 - Integrated Concepts Singly charged gas ions are...Ch. 19 - Integrated Concepts The temperature near the...Ch. 19 - Integrated Concepts (a) What is the average power...Ch. 19 - Integrated Concepts A lightning bolt strikes a...Ch. 19 - Integrated Concepts: A 12.0 V battery-operated...Ch. 19 - Integrated Concepts A battery-operated car...Ch. 19 - Integrated Concepts Fusion probability is greatly...Ch. 19 - Unreasonable Results (a) Find the voltage near a...Ch. 19 - Construct Your Own Problem Consider a battery used...Ch. 19 - Show that units of Vim and N/C for electric field...Ch. 19 - What is the strength of the electric field between...Ch. 19 - The electric field strength between two parallel...Ch. 19 - How far apart are two conducting plates that have...Ch. 19 - (a) Will the electric field strength between two...Ch. 19 - The voltage across a membrane forming a cell wall...Ch. 19 - Membrane walls of living cells have surprisingly...Ch. 19 - Two parallel conducting plates are separated by...Ch. 19 - Find the maximum potential difference between two...Ch. 19 - A doubly charged ion is accelerated to an energy...Ch. 19 - An electron is to be accelerated in a uniform...Ch. 19 - A 0.500 cm diameter plastic sphere, used in a...Ch. 19 - What is the potential 0.530 x 10-10 m from a...Ch. 19 - (a) A sphere has a surface uniformly charged with...Ch. 19 - How far from a 1.00 C point charge will the...Ch. 19 - What are the sign and magnitude of a point charge...Ch. 19 - If the potential due to a point charge is 5.00 102...Ch. 19 - In nuclear fission. a nucleus splits roughly in...Ch. 19 - A research Van de Graaff generator has a 2.00-rn-...Ch. 19 - An electrostatic paint sprayer has a...Ch. 19 - In one of the classic nuclear physics experiments...Ch. 19 - (a) What is the potential between two points...Ch. 19 - Unreasonable Results (a) What is the final speed...Ch. 19 - (a) Sketch the equipotential lines near a point...Ch. 19 - Sketch the equipotential lines for the two equal...Ch. 19 - Figure 19.28 shows the electric field lines near...Ch. 19 - Sketch the equipotential lines a long distance...Ch. 19 - Sketch the equipotential lines in the vicinity of...Ch. 19 - Sketch the equipotential lines in the vicinity of...Ch. 19 - Sketch the equipotential lines surrounding the two...Ch. 19 - (a) Sketch the electric field lines in the...Ch. 19 - The naturally occurring charge on the ground on a...Ch. 19 - The lesser electric ray (Narcine bancroftii)...Ch. 19 - What charge is stored in a 180 F capacitor when...Ch. 19 - Find the charge stored when 5.50 V is applied to...Ch. 19 - What charge is stored in the capacitor in Example...Ch. 19 - Calculate the voltage applied to a 2.00 F...Ch. 19 - What voltage must be applied to an 8.00 nF...Ch. 19 - What capacitance is needed to store 3.00 C of...Ch. 19 - What is the capacitance of a large Van de Graaff...Ch. 19 - Find the capacitance of a parallel plate capacitor...Ch. 19 - (a) What is the capacitance of a parallel plate...Ch. 19 - Integrated Concepts A prankster applies 450 V to...Ch. 19 - Unreasonable Results (a) A certain parallel plate...Ch. 19 - Find the total capacitance of the combination of...Ch. 19 - Suppose you want a capacitor bank with a total...Ch. 19 - What total capacitances can you make by connecting...Ch. 19 - Find the total capacitance of the combination of...Ch. 19 - Find the total capacitance of the combination of...Ch. 19 - Unreasonable Results (a) An 8.00 F capacitor is...Ch. 19 - (a) What is the energy stored in the 10.0 F...Ch. 19 - In open heart surgery. a much smaller amount of...Ch. 19 - A 165 F capacitor is used in conjunction with a...Ch. 19 - Suppose you have a 9.00 V battery, a 2.00 F...Ch. 19 - A nervous physicist worries that the two metal...Ch. 19 - Show that for a given dielectric material the...Ch. 19 - Construct Your Own Problem Consider a heart...Ch. 19 - Unreasonable Results (a) On a particular day, it...
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