removed trailing spaces from ReadMe.txt input

input/parallel_plate_capacitor/ReadMe.txt

@@ -1,22 +1,22 @@
 ###################################
 #### parallel_plate_capacitor #####
 ###################################
- 
-  -This example models a parallel plate capacitor such that 
-   a voltage of 10 V is specified at Zmax boundary and 0 V 
+
+  -This example models a parallel plate capacitor such that
+   a voltage of 10 V is specified at Zmax boundary and 0 V
    is specified at Zmin boundary.
-  
+
   -First four examples provided in this folder show different ways
    to specify these voltages.
 
-     1) inhomo_const_dirichlet: 
+     1) inhomo_const_dirichlet:
             This example specifies voltages directly through where
         boundary conditions are specified, e.g. dir(10) or dir(0).
 
      2) function_parsed_dirichlet:
-            This example specifies voltages through dirichlet function 
+            This example specifies voltages through dirichlet function
         parsers whose name is specified at the time of specifying boundaries,
-        e.g. dir(Zmin) or dir(Zmax). Function parsers are specified for 
+        e.g. dir(Zmin) or dir(Zmax). Function parsers are specified for
         Zmin and Zmax.
 
      3) function_parsed_robin:
@@ -27,33 +27,33 @@
             This example is similar to example 2 but voltage at the top plate
         is applied as a cosine function 10*cos(2 pi x/(2Lx)).
 
-  -Fifth example, is for the case with two dielectrics, where in upper Lz/2 region there is air 
+  -Fifth example, is for the case with two dielectrics, where in upper Lz/2 region there is air
    and in the lower, SiO2, epsilon_2 = 3.8.
 
-  -On all lateral sides we can either specify Neumann boundaries 
+  -On all lateral sides we can either specify Neumann boundaries
    or periodic boundaries.
 
 For verification:
 -Check that voltage in the ghost cells is as specified.
--Note: 
+-Note:
  Charge on the plate, Q = C V_0 (where V_0 = 10 V in our case)
- Surface charge density, sigma = Q/A (A = 0.2**2 in our case) 
+ Surface charge density, sigma = Q/A (A = 0.2**2 in our case)
  From Gauss' law, sigma = D (D_z in our 1-D example)
  For single dielectric, D_z = E_z / epsilon_0
- 
+
  From above equations, E_z = D_z/epsilon_0  = sigma/epsilon_0 = Q/(A*epsilon_0) = (C V_0)/(A*epsilon_0)
- So, C = E_z *A*epsilon_0 / V_0 
- 
+ So, C = E_z *A*epsilon_0 / V_0
+
  Now from solution, we can find that |E_z| = 200 V/m
  By calculating, we obtain C = 7.04 pF (as expected from theory).
 
 -For the two dielectric case:
  potential phi at the interface is given by,
- phi_int = epsilon_1 d_2 / (epsilon_2 d_1 + epsilon_1 d_2) V_0 
- 
+ phi_int = epsilon_1 d_2 / (epsilon_2 d_1 + epsilon_1 d_2) V_0
+
  In our example, epsilon_1 = epsilon_0 and epsilon_2 = 3.8*epsilon_0, d_1 = d_2 = L_z/2
  this gives, phi_int = 2.04 V
- 
+
  By probing cell-centered phi at the air-dielectric interface we find this phi_int = 2.07 V.
 
 -E_z in the air and dielectric can also be easily estimated by taking the gradient, e.g.
@@ -62,4 +62,4 @@ For verification:
  These values are close to what we see from the solution.
 
 
- 
+