The Law of Biot-Savart shows that the magnetic field of an
infinitesimal current element decreases as 1/r^2. Is there anyway
you could put together a complete circuit (any closed path of
current-carrying wire) whose field exhibits this same 1/r^2
decrease in magnetic field strength? Explain your reasoning.
a) Consider a plane strain formulation. Show that the plain
strain problem satisfies the
following equation:
??(?? + ??) = −?/? − ?
(???/?? + ???/??)
b) Consider a plane stress formulation. Show that the plain stress
problem satisfies the
following equation:
??(?? + ??) = −(? + ?)
(???/?? + ???/??)
(Hint: You may use the equations given below
?????? ∶ ??? = ??,? + ??,?
??????: ??? = 2???? + ???????
?????? ???????????: ???,? + ?? = 0...
Show that Maxwell's displacement current must be introduced to
satisfy continuity equation using Gauss' Law, Ampere-Maxwell law
and the fact that divergence of a curl of a vector is 0.