Since you tagged this as Version 10, we know you are using the Classic Designer, and thus Javascript is going to be a valid option.

Here's an example of some code that populates an email into an email field that has class name of myEmailField based on the selections in a drop-down field that has class name of myDropdownField.

//Note that this code assumes that there is only a single field with the
//myDropdownField class name - it won't work as expected if there is more
//than one.

$(document).ready(function() {
  
  //Make the department email field readonly.  Doing it here instead of
  //on the Layout page means it will allow changes via code.  If it's 
  //readonly from the Layout page, the changes won't save.
  $('.myEmailField input').attr('readonly', 'true');
  
  //When the Department dropdown changes, populate the department email field.
  $('.myDropdownField select').change(function() {
    var dropdownSelect = $(this).val();
    if (dropdownSelect == 'Accounting') {
      $('.myEmailField input').val('accounting@fakeaddress.com');
    }
    else if (dropdownSelect == 'Finance') {
      $('.myEmailField input').val('finance@fakeaddress.com');
    }
    else if (dropdownSelect == 'Marketing') {
      $('.myEmailField input').val('marketing@fakeaddress.com');
    }
    else if (dropdownSelect == 'IT') {
      $('.myEmailField input').val('it@fakeaddress.com');
    }
    else if (dropdownSelect == 'Management') {
      $('.myEmailField input').val('management@fakeaddress.com');
    }
  });
  
});

If you want to share specifics of the fields/options you are using and the results you need, I can provide a more tailored Javascript solution.