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Commit 87b07add authored by Erik Strand's avatar Erik Strand
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Add pset 11 questions

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---
title: Problem Set 11
---
## (14.1)
{:.question}
Do a Taylor expansion of equation (14.6) around V = 0.
## (14.2)
{:.question}
Problem 6.5 showed that for a Kibble balance the current I measured in the dynamic phase and the
voltage V measured in the static phase are related to the mass m, gravitational constant g, and
velocity v by $$IV = mgv$$. Using the inverse AC Josephson effect (equation 14.25) to determine the
voltage, and the quantum Hall effect (equation 13.41) along with the inverse AC Josephson effect to
determine the current, relate the measurement to fundamental constant(s).
## (14.3)
{:.question}
If a SQUID with an area of $$A = 1 cm^2$$ can detect 1 flux quantum, how far away can it sense the
field from a wire carrying 1 A?
## (14.4)
{:.question}
Typical parameters for a quartz resonator are $$C_e = 5 \si{pF}$$, $$C_m = 20 \si{fF}$$, $$L_m = 3
\si{mH}$$, $$R_m = 6 \si{\ohm}$$. Plot, and explain, the dependence of the reactance (imaginary part
of the impedance), resistance (real part), and the phase angle of the impedance on the frequency.
## (14.5)
{:.question}
If a ship traveling on the equator uses one of John Harrison’s chronometers to navigate, what is the
error in its position after one month? What if it uses a cesium beam atomic clock?
## (14.6)
{:.question}
GPS satellites orbit at an altitude of 20,180 km.
### (a)
{:.question}
How fast do they travel?
### (b)
{:.question}
What is their orbital period?
### (c)
{:.question}
Estimate the special-relativistic correction over one orbit between a clock on a
GPS satellite and one on the Earth. Which clock goes slower?
### (d)
{:.question}
What is the general-relativistic correction over one orbit? Which clock goes
slower?
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