One page.
The cover letter
A business-school cover letter should make the case, not repeat the file. Unless the advertisement asks for something different, one disciplined page is enough.
Your cover letter is not a second research statement. It is not a compressed teaching philosophy. It is not the place to narrate every stage of graduate school.
It has one job: tell the committee why this record belongs in this search.
Use the first paragraph to identify the position, your current role or degree timing, your field, and the central claim of the candidacy. The committee should know what you are applying for and what kind of scholar or teacher it is about to meet.
Use the next paragraph for research. Name the problem you study, the job-market paper, the strongest evidence, and the direction of the program. Do not list every project. The CV and research statement hold the inventory. The letter gives the argument.
Use the next paragraph for teaching and fit. State what you have taught, what you are prepared to teach, and why that meets the position. Connect yourself to the institution through the work: courses, students, program needs, or a relevant research link. Do not praise the school with adjectives that could describe any university.
Then close. Say the required materials are enclosed. Provide contact information if needed. Do not write a final paragraph about your lifelong dream of becoming an educator unless the sentence adds evidence the committee does not already have.
Paragraph 1: position, status, field, central candidacy. Paragraph 2: research question, job-market paper, evidence, next work. Paragraph 3: teaching record, courses you can cover, specific connection to the search. Paragraph 4: materials and direct close. This is a structure model, not text to copy.
Cut the biography. Cut the paragraph that explains why the discipline matters to society. Cut the list of every method you have used. Cut the summary of material that already has its own document. Cut any sentence that exists only to say you are excellent, passionate, dynamic, innovative, or collaborative.
Keep proof. A clear publication status. A defined research question. A course actually taught. A reason this line fits. A date the degree will be complete. Those details help a committee decide.
One page also tests whether you can identify the case. If you need three pages to explain why you fit, the problem may not be space. It may be that you have not decided what the committee should remember.
Follow the advertisement over any general rule. If the school asks for a longer letter or specific questions, answer them. Otherwise, respect the reader. Make one page do its work.