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.
Starting with Maxwell's equations show that the magnetic field
satisfies the same wave equation as the electric field. in
particular, that is, too, propagates with the same speed.
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.