Yes, you can cast spells without your spellbook. And yes, your list of prepared spells will stay prepared until you prepare a new list. In the Preparing and Casting spells section, only preparing a new list of spells actually requires your spellbook.
Do wizards cast spells?
Wizards can cast anything they have prepared, provided they have the requirements listed in the spell. Those include things like material components, focus, the ability to speak or do somatic gestures, and anything else that a spell might list. Spellbooks are never listed for the Wizard class.
What happens to a wizard when they lose their spellbook?
There’s a section in the 5e wizard class description in the PHB outlining exactly what the process is. A wizard can preemptively make a duplicate spellbook in such case, and it takes 50% of time and gold cost per spell to copy since they know the spell so well. I also know they can cast Cantrips whenever they’d like and as often as they’d like.
How do you cast wizard spells in dungeons and Dragons?
The Wizard table shows how many spell slots you have to cast your wizard spells of 1st level and higher. To cast one of these spells, you must expend a slot of the spell’s level or higher. You regain all expended spell slots when you finish a long rest. You prepare the list of wizard spells that are available for you to cast.
How long does it take to make a wizard spell list?
Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.
How do Wizards get bonus spell slots from intelligence?
You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell). The spells must be of a level for which you have spell slots.
