Copy down in column - vba

Question

I have a problem with a part of a bigger VBA Macro, so no; I can not do this another way.
I want to copy a value down in an empty column, but only in as many rows as I have in the worksheet.
I want it to automatically count how many rows that is active in the worksheet and that that row as the last one, but I get stuck and it does not want to do as I want.
Below is the code that I am working with.
Sub Coppy_down()
Range("B3").Formula = "=Mid(A1, 11, 2)"
Range("B3").Value = Range("B3").Value
Range("B3").Copy Range("B3", Range("B" & Rows.Count).End(xlUp))
End Sub
My data looks as this (I did not find how to attach)
A B
1 District: SE
2 Date District
3 8/17/2018
4 8/24/2018
5 8/31/2018
6 9/7/2018
7 9/14/2018
8 9/21/2018
9 9/28/2018
And I want to fill cell B3:B9 with SE, but not that it might be B3:B4 or B3:B15, so it need to be flexible.
Thanks

Answer 1

Find the last populated row of column A, by coming up from the bottom of the sheet, and use that for column B in the "fill down". I have used Right$ in place of your Mid. You could also use Mid$(.Range("A1").Value, 11, 2). The formula steps are unnecessary and can be removed.
Change the sheet name to the appropriate sheet name.
Sub TEST()
With ThisWorkbook.Worksheets("Sheet2")
.Range("B3").Formula = "=RIGHT(A1,2)"
.Range("B3").Value = .Range("B3").Value
If .Cells(.Rows.Count, "A").End(xlUp).Row > 3 Then
.Range("B4:B" & .Cells(.Rows.Count, "A").End(xlUp).Row) = .Range("B3")
End If
End With
End Sub
You could simplify, my preference, to:
Option Explicit
Public Sub TEST()
With ThisWorkbook.Worksheets("Sheet2")
If .Cells(.Rows.Count, "A").End(xlUp).Row >= 3 Then
.Range("B3:B" & .Cells(.Rows.Count, "A").End(xlUp).Row) = Right$(.Range("A1"), 2)
End If
End With
End Sub

Answer 2

One slight amendment to QHarr's solution:
You should either force a worksheet.calculate or use a VBA formula when pasting values. If not you will get blanks if the manual recalculation setting is used. For example
Sub Coppy_down()
With Sheet1
.Range("B3", .Range("B" & .Cells(Rows.Count, "A").End(xlUp).Row)).Value = Mid(.Range("A1").Value, 11, 2)
End With
End Sub