scripts/TP2 10.28 Potential of a charged sphere.LACE

   1 # Determine the potential (inside and outside) of a charged sphere (radius R) with a constant internal charge density rho0.
   2 #
   3 # phi(r)'' = -rho0/epsilon0 - 2/r * phi(r)'
   4 #   with rho0 = 0 outside of sphere
   5 #   using t as variable for r
   6 #
   7 # compound functions used:
   8 # Open Amplifier
   9 define openamp (weight*: variable-1, weight*: variable-2) -> output
  10   isum (weight*: variable-1, weight*: variable-2) -> output
  11     connect (FB:) -> GND
  12
  13 # Division
  14 define idivide (numerator, denominator) -> -quotient
  15   openamp (numerator, product) -> -quotient
  16   multiply (-quotient, denominator) -> product
  17
  18 # coefficients
  19 coefficient.1      -> factor0,2 # shall be set to 0.2
  20 coefficient.2 (-1) -> -rho0/epsilon0
  21 coefficient.3 (-1) -> -phi0
  22 coefficinet.4 (-1) -> -R        # -radius of sphere
  23
  24 # generate a ramp of t
  25 iintegrate (-1) -> t
  26
  27 # distinguish in sphere or outside
  28 compare (t, -R) -> -rho/epsilon0_l
  29   LT0: -rho/epsilon0   # in sphere,
  30   GT0: GND             # outside sphere
  31
  32 # calculate phi
  33 iintegrate (1*: -rho0/epsilon0_l, 10*: -0.2/r*phi') -> -phi' # need 2/r*phi' thus 10* input
  34 iintegrate (-phi') -> phi
  35   IC: -phi0
  36 invert(-phi') -> phi'
  37
  38 # doing this division by t first because phi' is low when also t is, thus there is the chance of less overload
  39 idivide (phi', t) -> -phi'/t
  40 cmultiply (-phi'/t, factor0.2) -> -0.2/r*phi'
  41
  42 output(t)     -> out.x
  43 output(phi')  -> out.y
  44 output(phi)   -> out.z