THE FIELDS OF MOVING CHARGES — Edward Purcell & David Morin
Physics — E&M · laminated-conductor-extremum
Problem
Laminated conductor extremum **
(a) Consider the setup in Problem 4.5. For given conductivities of the two materials, show that the ratio σ⊥/σ∥ is minimum when the layers have the same thickness (independent of what the conductivities are).
Give a physical argument why you would expect σ⊥/σ∥ to achieve a maximum or minimum somewhere between the two extremes where one thickness is much larger/smaller than the other.
(b) For given layer thicknesses, show that the ratio σ⊥/σ∥ is maximum when the materials have the same conductivity (independent of what the thicknesses are).
Give a physical argument why you would expect σ⊥/σ∥ to achieve a maximum or minimum somewhere between the two extremes where one conductivity is much larger/smaller than the other.