Download PHYS 354 Electricity and Magnetism II Problem Set #1

PHYS 354
Electricity and Magnetism II
Problem Set #1
1. Vector Calculus
Show that
  1
 x   
 xy




 
xy
 3
xy


where x is the field coordinate and y is the source coordinate.
2. Biot-Savart Law in differential form
Show that the Biot-Savart Law in integral form
 

Bx   0
4
 
 
xy
 d y J  y   x  y 3
3
can be reduced to the magnetostatic differential form used by Maxwell
 

  B  0 J .
3. Magnetic Vector Potential
Two long, thin, straight wires parallel to the z-axis carry currents  I and  I . Calculate the vector


potential A by integrating both wires from z  a to z  b and letting a, b   . Show that A is

parallel to the z-axis and that the expression for A in terms of r1 and r2 (the distances from the two
wires) is
2
  I r 
A  0 ln  2  kˆ .
4  r1 