Homework Set # 3 - Due September 16



     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).

  Solution (pdf file)

     6)  3.9.1


  7) Click here to see the problem