TABLE OF CONTENTS In the previous chapter we considered the special case of Maxwell's equations with time-harmonic sources. If the field sources have arbitrary time dependence, then we must work with the time-dependent curl and divergence equations
| (7.1) |  |
where J e = ? E + J source and ( ?, ?) = ( ? r ? 0 , ? r ? 0).
The simplest example of transient current induction is that produced by a magnetic field tangential to a conducting half-space that is switched on at t = 0.
This field can be thought of as being produced by an infinite sheet with a uniform surface current density that is parallel to the conducting half-space. Neglecting the displacement current we have
| (7.2) |  |
inside the metal and taking the curl of this equation and using
| (7.3) |  |
we obtain
| (7.4) |  |
For an external field B( t) = B 0 ?( t) j, the differential equation with initial conditions becomes
| (7.5) |  |
where ?( t) is zero for t < 0 and 1 for t ? 0. Taking the Laplace transform of both the differential equation and initial conditions gives
| (7.6) |  |
where B y (0) = 0. The solution to this equation is
| (7.7) |  |
Applying the boundary conditions we have A = 0 and 
giving
| (7.8) |  |
Performing the inverse Laplace transform in MATLAB
%MATLAB code for performing the inverse...
