Is it reasonable that a manager who is successful in a certain field, to be successful in a different field that he has no experience in?

Yes it is. Firstly, though the manager must do some research to understand the fundamental differences between this new field and his/her prior fields. Equipped with an understanding and basic knowledge this person can keep building on his/her learning with experience every day. Beyond a certain stage, your overall understanding and perspectives on general management help you manage diverse fields. It gives you a sharper and quicker uptake on problem solving too...

No it is not compulsory.  Though a successful manager in one certain field may have a bright chances of succeeding in other fields also due to his / her previous experiences.  In case if the field is related to a specific technology which the manager is unaware then he/she has to rely on inputs from other sources.