How to delete some lines in streamplot

Question

my name is Michael and im new to this Forum, so sorry for any misbehavior (also english is not my native language).

My Question:

I have a given (quite difficult) electrical field and i want to make a Streamplot.

This are my Functions:

Ey1 := -\[Sigma] (Log[
  a - x + Sqrt[(-a + x)^2 + (a - y)^2 + (z - d)^2]] + 
 Log[-a + x + 
   Sqrt[(-a + x)^2 + (a + y)^2 + (z - d)^2]]) + \[Sigma] (Log[-a -
    x + Sqrt[(a + x)^2 + (a - y)^2 + (z - d)^2]] + 
 Log[a + x + Sqrt[(a + x)^2 + (a + y)^2 + (z - d)^2]])

Ey2 := \[Sigma] (Log[
      a - x + Sqrt[(-a + x)^2 + (a - y)^2 + (z + d)^2]] + 
     Log[-a + x + 
       Sqrt[(-a + x)^2 + (a + y)^2 + (z + d)^2]]) - \[Sigma] (Log[-a -
        x + Sqrt[(a + x)^2 + (a - y)^2 + (z + d)^2]] + 
     Log[a + x + Sqrt[(a + x)^2 + (a + y)^2 + (z + d)^2]])

Ez1 := \[Sigma] (ArcTan[((a - x) (-a + y))/((z - 
         d) Sqrt[(a - x)^2 + (-a + y)^2 + (z - d)^2])] + 
     ArcTan[((a + x) (-a + y))/((z - 
         d) Sqrt[(a + x)^2 + (-a + y)^2 + (z - 
          d)^2])]) - \[Sigma] (ArcTan[((a - x) (a + y))/((z - 
         d) Sqrt[(a - x)^2 + (a + y)^2 + (z - d)^2])] + 
     ArcTan[((a + x) (a + y))/((z - 
         d) Sqrt[(a + x)^2 + (a + y)^2 + (z - d)^2])])

Ez2 := -\[Sigma] (ArcTan[((a - x) (-a + y))/((z + 
         d) Sqrt[(a - x)^2 + (-a + y)^2 + (z + d)^2])] + 
     ArcTan[((a + x) (-a + y))/((z + 
         d) Sqrt[(a + x)^2 + (-a + y)^2 + (z + 
          d)^2])]) + \[Sigma] (ArcTan[((a - x) (a + y))/((z + 
         d) Sqrt[(a - x)^2 + (a + y)^2 + (z + d)^2])] + 
     ArcTan[((a + x) (a + y))/((z + 
         d) Sqrt[(a + x)^2 + (a + y)^2 + (z + d)^2])])

This is my Plot so far:

Show[StreamPlot[{Ez1 + Ez2, Ey1 + Ey2} /. {a -> 10, 
x -> 0, \[Sigma] -> 1, d -> 2}, {z, -15, 15}, {y, -15, 15}],Graphics[{Red, Line[{{-2, -10}, {-2, 10}}], Red, Line[{{2, -10}, {2, 10}}]}]]

As you can see i have highlightet some lines, that does not start on the plate.

Is there any way to get rid of this lines ?

I tried to work with DeleteCase, but it was not successful.

Thx, Michael

Answer 1

When such things matter it might be easier to specify the "stream points," instead of fixing what the default setting does:

sp = Join[
   Table[{-3, y}, {y, -10, 9, 1}],
   Table[{3, y}, {y, -10, 9, 1}],
   Table[{0, y}, {y, -10, 9, 1}]
   ];

Show[
 StreamPlot[
  {Ez1 + Ez2, Ey1 + Ey2} /. {a -> 10, x -> 0, \[Sigma] -> 1, d -> 2},
  {z, -15, 15}, {y, -15, 15}, StreamPoints -> sp
  ],
 Graphics[{Red, Line[{{-2, -10}, {-2, 10}}], Red, Line[{{2, -10}, {2, 10}}]}]
 ]