The former president is leasing part of his family's farmland for a project that is both cutting edge and homespun. The solar panels — 3,852 of them — shimmered above 10 acres of Jimmy Carter’s soil where peanuts and soybeans used to grow. The panels moved almost imperceptibly with the sun. And they could power more than half this small town, from which Carter rose from obscurity to the presidency. Nearly 38 years after Carter installed solar panels at the White House, only to see them removed during Ronald Reagan’s administration, the former president is leasing part of his family’s farmland for a project that is both cutting edge and homespun. It is, Carter and energy experts said, a small-scale effort that could hold lessons for other pockets of pastoral America in an age of climate change and political rancor.