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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?