Homework Set # 3 - Due September 17
1 ) Click
here to see the problem
2) 3.5.6
3) Unit vectors in non-Cartesian coordinate systems are usually
functions of the coordinate variables, ei=(q1,q2,q3)
|ei|=1.
Show that either ∂ei/∂qj=0
or ∂ei/∂qj
is
orthogonal to ei.
Hint:
∂ei2/∂qj=0.
Solution
(pdf file)
4) 3.6.2
(Hint: use the result of 3.5.9 provided in the book)
Solution
(pdf file)
5) In a steady state
the magnetic field H
satisfies the Maxwell equation curl H=J,
where J
is the current density. At the boundary between two media there is a
surface current density K.
Show that a boundary condition on H
is
n x (H2-H1)=K.
n is a unit vector normal to the surface and out of medium 1. Hint: Consider a narrow loop perpendicular to the interface as shown in the Figure and a.(bxc)=b.(cxa).