if you had a contract it will state it in there, if not its a case of being understanding and realistic, How long have you worked for your current employer, how many staff do they employ and is there anyone there to step up into your vacated position, have they been good employers?. Ideally a notice of your attention to quit with the understanding that you would be be prepared to hold the fort until your replacement could be found. That could be as little as a fortnight in the case of promotion of an existing employee or a minimum of a month if the post has to be advertised, six weeks would be reasonable on your part to allow your counterpart to bed in, but most employers would wish to move on quickly once someone in a management post has declared their intention to part. Remember it is polite to be as accommodating as possible since any new potential future position would look back to previous employment and how you conducted yourself.
This said you are posting on a cancer site so health issues may be forcing your hand, be upfront about this to your employer and most would be overly understanding and appreciate ongoing issues may force your hand, honesty is always the best policy,
As a manager in a livestock sector l always worked with my then employer and always left on good terms when a replacement was found , my new employer would understand and work with that because what goes round might come round for them in the future
