Honors Calculus 252-2

Winter 2002
Hermann Riecke

Problem Set 5


to be handed in Friday February 15, 2002, in class



  1. The electric field due to a point charge, q, at the origin is


    E = q
    ^
    R
    R2
    		       R =   ________
    Öx2+y2+z2
     
    		        ^
    R
     
    		 = (x,y,z)
    R
    		 .

    1. Compute the flux of the electric field,


      ó
      õ       		ó
      õ

      S 
      		 E ·n  dS  ,
      for a sphere of radius A centered at the origin.

    2. Compute the flux of the electric field for a cylinder of radius a and height 2b centered at the origin.

    3. Gauss' Law states the flux of an electric field through a closed surface is proportional to the charge inside the surface. Comment on how this relates to the results in (a) and (b).

  2. 8.3.1iv,

  3. 8.3.2

  4. 8.3.8 Note: the force exerted by charge q1 on charge q2 at locations r1 and 2, respectively, is given by


    F = q1 q2
    4pe0
    		 R
    |R|3
    		        where       R = r2-r1,
    		(1)
    e0 is the dielectric constant of vacuum.

  5. 8.3.11

  6. 8.4.1

  7. 8.4.5, 8.4.14 Note: do not evaluate these expressions componentwise.

  8. 8.4.11



File translated from TEX by TTH, version 2.78.
On 12 Feb 2002, 11:01.