A new law legalizing medical marijuana in Massachusetts is challenging communities north of Boston to write new zoning identifying areas where shops distributing the substance may — or may not — open after the new law takes effect on Jan. 1.

Proposals vary widely, from bans in Reading, Wakefield, and potentially Melrose, to zoning amendments proposed in Malden, Salem, and Woburn, and to restricting medical marijuana dispensaries to Route 1 in Peabody.