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The leadership role fell to Root after discussions with vice-captain Harry Brook.
"It became pretty obvious that after talking to both Joe and Harry, that Joe was the right person to do it," said McCullum.
"He's actually excited, because while he gave it everything he could last time around, he feels he's in a much better place now."
McCullum noted that Brook will assist Root tactically.
"He made mention to me that he feels Harry Brook's got arguably one of the best tactical brains that he's seen, so he'll be leaning heavily on Harry."
England won the opening match at Lord's, taking a 1-0 lead in the three-match series. The squad completed their first training session on Sunday with a calm atmosphere.
"Joe spoke brilliantly as well. We know how calm a personality he is," McCullum said.
The match is part of the 2025-27 World Test Championship cycle.
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England's official lineup: Ben Duckett, Emilio Gay, Jacob Bethell, Joe Root (c), Harry Brook, Jamie Smith (wk), Jordan Cox, Jofra Archer, Josh Tongue, Matthew Fisher, Sonny Baker.
