COLUMBUS, Ohio — When the top Democratic presidential hopefuls take the debate stage Tuesday, America will see a race that has changed dramatically since the candidates faced off just a month ago.

The new dynamics include Joseph R. Biden fending off accusations of nepotism and corruption involving his son Hunter, Sen. Bernard Sanders of Vermont striving to demonstrate vitality after suffering a heart attack, billionaire Tom Steyer seizing a spot for the first time in the debate limelight and Sen. Elizabeth Warren of Massachusetts surging to the front in leadoff states by running against the uber wealthy.

What’s more, the political drama on stage will be overshadowed by House Democrats’ impeachment inquiry targeting President Trump.

The burning question when Democrats took the stage for the September debate in Houston was whether anyone would knock Mr. Biden from his front-runner perch.

“We are in a different world than we were when the last debate occurred,” said Christopher P. Borick, political science professor and director of the Muhlenberg College Institute of Public Opinion.

He expects the impeachment inquiry and the U.S. pullout in Syria to drive part of the discussion Tuesday on the debate stage at Otterbein University in Westerville, Ohio, just outside Columbus.

Mr. Biden also must be prepared to answer more questions about his son’s business dealings in Ukraine and China while he was vice president.

“He can’t just ignore it. He has to respond and how he responds and to what degree [he responds] are going to be central to his prospects moving forward,” Mr. Borick said.

In the run-up to the debate, Mr. Biden attempted a preemptive strike at the Hunter Biden issue, including outlining an ambitious anti-corruption plan he said he would implement if elected.

Hunter Biden announced over the weekend that he would step down from the board of a Chinese-backed firm. He also agreed to an interview Tuesday with ABC News to address questions about his overseas business deals while his father was vice president.

Hunter Biden sealed the more than $1 billion deal with a Chinese-backed firm after flying to China with his father aboard Air Force Two.

Another foreign deal — Hunter Biden’s $600,000-a-year job on the board of a Ukraine gas company — is at the heart of House Democrats’ impeachment inquiry, which now has the overwhelming support of Democratic primary voters — including a majority of the party’s voters in the early primary states that say Mr. Trump should be locked up.

Mr. Trump in July requested the Ukraine president investigate the Bidens, a request that prompted a whistleblower complaint that Mr. Trump was abusing his Oval Office power to dig up dirt on a political foe. The whistleblower, who is believed to be a CIA official who was assigned to the White House, spurred the Democrats’ impeachment inquiry.

Mr. Trump said he made a legitimate request for a corruption probe.

Mr. Biden has insisted that he, too, did nothing wrong and says the episode demonstrates that Mr. Trump is afraid of him.

“If I am your next president I’m going to build on the squeaky clean, transparent environment that we had in the Obama-Biden White House,” Mr. Biden said in Iowa. “No one in my family will have an office in the White House, will sit in on meetings as if they’re a Cabinet member, will in fact have any business relationship with anyone that relates to a foreign corporation or foreign country.”

Mr. Biden’s rivals for the nomination have avoided criticizing him directly for his son’s apparent sweetheart deals, in part to avoid the appearance of siding with Mr. Trump.

However, several have said they wouldn’t let their VP’s son engage in questionable foreign ventures.

“Whether fair or not, the allegations against Biden have put him on the defensive and assisted the surging Elizabeth Warren,” said Mark J. Rozell, dean of the Schar School of Policy and Government at George Mason University.

Indeed, Ms. Warren has been on the rise, but also has faced scrutiny over her claim that she was pushed out of a teaching job in the 1970s because she was visibly pregnant.

Meanwhile, Mr. Sanders’ recent health scare has reintroduced a question potentially damaging to the 78-year-old’s candidacy: How old is too old to be president?

Mr. Rozell said that could create an opening for one of the lower-tier candidates to make their mark on the race.

South Bend Mayor Pete Buttigieg has been lingering just behind the front-runners and has recently showed a greater willingness to challenge his rivals, signaling he could take a more aggressive approach.

Mr. Steyer will get his first chance to introduce himself and his vision to a national television audience after entering the race late and failing to qualify for the three opening debates.

“Tom will highlight what makes him different from other candidates on stage,” Steyer campaign manager Heather Hargreaves said Monday.

The debate will feature 12 candidates — more than any of the previous candidate showdowns.

Rounding out the list of debate participants are: Sen. Kamala D. Harris of California; Sen. Amy Klobuchar of Minnesota; Sen. Cory A. Booker of New Jersey; entrepreneur Andrew Yang; former Rep. Beto O’Rourke of Texas; and Rep. Tulsi Gabbard of Hawaii.

Ms. Gabbard had threatened to boycott the “so-called” debate, accusing the Democratic National Committee and the corporate media of conspiring to rig the primary race. But she caved Monday and said she will attend.

It was the latest example of how struggling candidates have tried to gin up interest in their campaigns.

“It’s still very early, and although a lot has changed very quickly, who knows what the race will look like in another week or two?” Mr. Rozell said.

• Seth McLaughlin reported from Washington.

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