Marblehead, Swampscott and Lynn voters go to the polls March 4 to pick a successor to state Rep. Douglas Petersen who starts his job as state agriculture commissioner today.Candidates have until Dec. 26 to submit 150 signatures of registered voters to local election officials. Election registrars will certify the signatures before sending them to the Secretary of State’s office on Jan. 2.The primary election is on Feb. 5. The names of candidates for party nomination will appear on the same ballot as presidential candidates.The 8th Essex District in the Massachusetts House consists of Marblehead, Swampscott and Ward 3, Precinct 4 and Ward 4, Precinct 4 in Lynn.Petersen was a 42-year-old Salem State College professor in 1990 when he beat four fellow Democrats and a Republican finalist to win the 8th District seat.Since then, the Marblehead resident has beaten back challenges from a succession of challengers. He sponsored environmental protection legislation during his House tenure and top state officials picked him for the agriculture post in October.His departure prompted Marblehead resident Lori Ehrlich to announce her candidacy on Nov. 7 for the House seat. She is involved in HealthLink, a local environmental group.Nomination papers are available at the Elections Division of the Secretary’s Office, Room 1705 of the McCormack State Office Building, One Ashburton Place, Boston, and at Lynn City Hall and the town halls of Marblehead and Swampscott.