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Commit 9e1970e3 authored by Erik Strand's avatar Erik Strand
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Answer 14.3

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...@@ -2,11 +2,13 @@ ...@@ -2,11 +2,13 @@
title: Problem Set 11 title: Problem Set 11
--- ---
## (14.1) ## (14.1)
{:.question} {:.question}
Do a Taylor expansion of equation (14.6) around V = 0. Do a Taylor expansion of equation (14.6) around V = 0.
## (14.2) ## (14.2)
{:.question} {:.question}
...@@ -16,12 +18,28 @@ velocity v by $$IV = mgv$$. Using the inverse AC Josephson effect (equation 14.2 ...@@ -16,12 +18,28 @@ velocity v by $$IV = mgv$$. Using the inverse AC Josephson effect (equation 14.2
voltage, and the quantum Hall effect (equation 13.41) along with the inverse AC Josephson effect to 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). determine the current, relate the measurement to fundamental constant(s).
## (14.3) ## (14.3)
{:.question} {:.question}
If a SQUID with an area of $$A = 1 cm^2$$ can detect 1 flux quantum, how far away can it sense the 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? field from a wire carrying 1 A?
As found in problem 6.4 in [problem set 4](/psets/04.html), the magnitude of the magnetic field a
distance $$r$$ away from an infinitely long and thin conductor carrying a current $$I$$ is $$I/(2
\pi r)$$. One flux quantum is $$\num{2.07e-7} \si{G \cdot cm^2}$$ i.e. $$\num{2.07e-11} \si{T \cdot
cm^2}$$. So to get one flux quantum over $$1 \si{cm^2}$$, we need a magnetic field of
$$\num{2.07e-11} \si{T}$$. Thus a one amp current can be detected at a distance of
$$
\begin{align*}
r &= \frac{\mu_o I}{2 \pi B} \\
&= \frac{\num{1.26e-6} \si{T m / A} \cdot 1 \si{A}}{2 \pi \cdot \num{2.07e-11} \si{T}} \\
&= \num{9.66e3} \si{m}
\end{align*}
$$
## (14.4) ## (14.4)
{:.question} {:.question}
...@@ -29,12 +47,14 @@ Typical parameters for a quartz resonator are $$C_e = 5 \si{pF}$$, $$C_m = 20 \s ...@@ -29,12 +47,14 @@ Typical parameters for a quartz resonator are $$C_e = 5 \si{pF}$$, $$C_m = 20 \s
\si{mH}$$, $$R_m = 6 \si{\ohm}$$. Plot, and explain, the dependence of the reactance (imaginary part \si{mH}$$, $$R_m = 6 \si{\ohm}$$. 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. of the impedance), resistance (real part), and the phase angle of the impedance on the frequency.
## (14.5) ## (14.5)
{:.question} {:.question}
If a ship traveling on the equator uses one of John Harrison’s chronometers to navigate, what is the 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? error in its position after one month? What if it uses a cesium beam atomic clock?
## (14.6) ## (14.6)
{:.question} {:.question}
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