A federal judge on Friday declared unconstitutional the state’s ultrasound requirement for women seeking abortions, saying it violated the First Amendment by requiring doctors to display a fetal image and describe it even to women who covered their eyes and ears. Judge Catherine C. Eagles of the Middle District of North Carolina called the law, passed in 2011, an impermissible attempt to compel doctors “to deliver the state’s message in favor of childbirth and against abortion.” The state has not said whether it will appeal to the Fourth Circuit, in Richmond, Va. A similar law in Texas was upheld by the Fifth Circuit, in New Orleans, and is in effect.