MS Excel / VBA help thread

I have a load of workbooks that I want to split out each worksheet into multiple files with each new workbook being one tab from the original workbook (with the filename the same as the tab).

There are loads of example macros for this online and they are all basically identical. However, they don't work for me. All I get is one new blank workbook called sheet1 (no tabs are named sheet1 and there are no hidden tabs).

Sub SplitWorkbook()
    Dim workbookPath As String
    workbookPath = Application.ActiveWorkbook.Path
    Application.ScreenUpdating = False
    Application.DisplayAlerts = False
    For Each wSheet In ThisWorkbook.Sheets
        wSheet.Copy
        Application.ActiveWorkbook.SaveAs Filename:=workbookPath & "\" & wSheet.Name & ".xlsx"
        Application.ActiveWorkbook.Close False
    Next
    Application.DisplayAlerts = True
    Application.ScreenUpdating = True
End Sub

It falls down at wSheet.copy. Any bright ideas what is going wrong, it looks like it should work.