diff --git a/_psets/11.md b/_psets/11.md new file mode 100644 index 0000000000000000000000000000000000000000..7c96ce1d3b91ea4b1ccc1c2031cb9ecc1a2ffcd0 --- /dev/null +++ b/_psets/11.md @@ -0,0 +1,63 @@ +--- +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?