WIK didn't look hard enough. The Prince William County zoning ordinance is linked at: http://www.pwcgov.org/default.aspx?topic=040073001420002653
Or go directly to this site:http://www.municode.com/Resources/gateway.asp?pid=14114&sid=46
Sec. 32-240.02. Applicability.
1. The requirements set forth in this part shall govern the location of commercial monopoles and towers that are 50 feet in height or greater, amateur radio towers, and satellite dish antennas, and shall establish performance standards for antennas and related equipment used in association with existing structures, roof tops, utility distribution structures, and replacement utility distribution structures that are designed to accommodate antennas and associated equipment. Commercial monopoles and towers that are less than 50 feet in height, and amateur radio towers less than 75 feet in height shall be permitted by right in all zoning districts, subject to the provisions of this part. The requirements set forth in this part shall also govern the use and location of individual commercial satellite dish antennas greater than 50 feet in height and/or greater than three feet in diameter and commercial satellite dish antenna earthstation installations with two or more dishes.
2. Telecommunications equipment for private residential use, including amateur radio service and satellite dishes shall be permitted in all districts as an accessory use. Other than the provisions of sections 32-240.10.2 through 32-240.10.4 and 32-240.11, the requirements set forth in this part shall not govern the use and location of amateur radio service towers that are 75 feet or less in height.
Sec. 32-240.11. Amateur radio service antennas, satellite dishes, and associated supporting structures for private residential use.
Amateur radio service antennas, satellite dishes, and associated supporting structures used for private residential use in any zoning district shall be allowed as accessory uses as follows:
1. Located in the rear and side yards only;
2. If less than 20 feet in height, setback a minimum of five feet from the rear and side property lines, and in the case of a corner lot, a minimum of 20 feet from the side property line adjacent to the street;
3. If greater than 20 feet in height, then subject to the yard and setback requirements of the zoning district in which the facility is located; and
4. If greater than 75 feet in height, then allowed with a special use permit.
Basically, at least theoretically, you're OK as far as the county is concerned. This doesn't override neighborhood restrictions, though.
I could not easily find out whether you would need a building permit. That would be a whole other issue.