• Homework 1: (due Monday Feb. 20 2012)
  

  
    Consider a dipole made up of a charge +q at the (x,y,z) coordinate (0,0,a/2) and a charge -q at (0,0, -a/2).
  
    The dipole moment is then p = aq.
  
  
  
    Find the electric field at a point (x,0,z) far away from the origin. You should consider the limit when r >> a
  
    where r2 = x2 + z2.  Express your result in terms of r and θ, where θ is the angle between the x-axis and
  
    the position at (x,0,z):   tan(θ) = z/x  so that  x = r cos(θ)  and  z = r sin(θ). 
  
  

• Homework 2: (due Monday Feb. 27 2012)
  

  
    A spherically symmetric charge of radius R has a charge density (per unit volume)  equal to ρ(r).
  
      (a) What must ρ(r) be so that the field inside ( r < R ) has a constant magnitude E0 ?
  
      (b) What is the total charge in a volume of radius r ?
  
      (c) Plot the quantities in parts (a) and (b) for all values of r.
  
    Repeat the parts (a), (b), and (c) above for an infinitely long cylindrical charge of radius R.
  
  

• Homework 3: (due Monday March 5 2012)
  

  
  Consider the two geometries in Homework 2. In both cases, assume that the potential at r = 0 is equal to zero.
  
  For both cases, find the potential as a function of r, and plot your results.
  
  

• Homework 4: (due Monday April 9 2012)
  

  
  Find the magnetic field on the axis of a rotating thin charged disk. The insulating disk is uniformly
  
  charged with a surface charge density (per unit area) σ  and has a radius R. The disk is rotating
  
  with angular velocity ω.
  
  

Check the Stars system for your homework grade. In some cases, you may be able to re-submit your homework to the assistant with corrections and improve your grade.