Add list column to list contenttype

$web = Get-SPWeb -Identity "URL to your site"
$list = $web.Lists["List name"]
$ct = $list.ContentTypes["Contenttype Name"]
$field = $list.Fields["Field Name"]
#$field = $list.Fields[{GUID}]
$fieldLink=New-Object Microsoft.SharePoint.SPFieldLink($field)
$ct.FieldLinks.Add($fieldLink);
$ct.Update()
$web.Dispose()