366 Week 10: Maxwell’s Equations and Light
between earth orbit and a lunar orbit, or between earth orbit and an orbit around/near
mars without the expenditure of fuel.
In a nutshell, what is the maximum plausible transverse acceleration one can expect to
achieve using a light sail of reasonable thickness angled atθwith respect to the sun, for a
payload of of (say) 1 metric ton (2000 kg)? How large a light sail do you need to achieve
that result?
The power output of the sun is 3. 8 × 1026 watts, and its mass is 2. 0 × 1030 kilograms. If
you need it, the mean radius of earth’s orbit isR= 1. 5 × 1011 meters.Problem 5.Consider a resistor capped with perfectly conducting ends. The resistor is a cylinder of
radiusaand lengthLand is filled with a material of resistivityρ. A voltageVis hooked
up across the resistor so that current flows.a) Find the net resistanceRof the resistor.
b) Find the currentIthrough the resistor.
c) Find the electric field inside the resistive material.
d) Find the magnetic field as a function of distance from the cylinder axis inside the
resistive material (assume that its permeability isμ 0 ).
e) Evaluate thePoynting vectorS~at an arbitrary point on thecylindrical surfaceof
the resistor.
f) Evaluate theflux of the Poynting vectorthrough that surface. Simplify it so that is
given in terms ofIandR. Surprise! The Poynting vectorprecisely predicts Joule
heating!