How to send a user an email when a content is published by somebody else?
The Workflow module can do it exactly what you want. By using this module you can trigger different action at each flow of content.


  Workflows are made up of workflow states. Transitions between states can be allowed per role. For example, a workflow with the states Draft, Review, and Published could be assigned to the Story node type. Only users with role 'chief editor' can set Stories to the published state.
  You can set up the Workflow to alter states from form, page, comment and a special workflow tab.