In the "Search for Issues" screen, there's a button called "Columns" on which controls what fields are to be displayed in the results. Uncheck everything that you don't need and then choose the option "Export (Current Fields).
What I don't understand however, is what you mean by "No issues to be exported, just the business area field information". Custom Fields are associated to issues, so you will have to export the issues with these custom field.
Ok, you can't do it, because JIRA works with issues, not projects. You can get close though. Filter for *"business area impacted" is empty*. Save the filter. Put a gadget on your dashboard called "filter statistics", selecting your saved filter, and "project" as the field to group by. You'll get a list of all projects that have issues using the field at least once. It won't list projects where the field *could* be used, but has not yet been used, and you'll have numbers on the graphs to tell you how much the field is actually used as well, but it should cover most of what you need there.
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